“I have visited this region many times,” our guide confided, “and I have never seen it like this before.” Fairies had painted the scene overnight, silvering it with frost and ice. Snow clung to the…

Shrimp for breakfast in Sapporo | Kittie Helmick | The Critic Magazine

Other factors included a poor public relations campaign that failed to overcome the negative outcomes of the COVID-delayed Tokyo 2020 Summer Games held in 2021, and concerns that a Winter Games budget could balloon

Report: Sapporo’s Winter Olympics bid failed in part due to too much snow

Saporo

saporo

Hey there! I'm Dominik Tomicevic, the founder and CEO of Memgraph. Back in 2011, I was one of just four people worldwide to receive the Microsoft Imagine Cup Grant, personally awarded by Bill Gates, for developing game-changing technologies in data processing. In 2016, I co-founded Memgraph, an open-source graph database designed for high-performance, real-time connected data processing. Our mission is to deliver knowledge graphs with unprecedented integration and ease of use, setting a new benchmark for knowledge graph solutions. Today, Memgraph boasts an open-source community of over 150,000 members and serves a portfolio of Global 2000 customers, including NASA, Cedars-Sinai, and Capitec Bank. On a personal note, I love making coffee and cocktails, and I nerd out about aviation. An ideal combo, right? In this post, I’ll answer the ten questions for startup founders from HackerNoon Founder and CEO David Smooke. 1. What is your company in 2–5 words? Open-source, in-memory graph database. 2. Why is now the time for your company to exist? The world runs on connected data, but existing databases are too slow, too clunky, or too expensive for real-time. With AI, fraud detection, and recommendation systems exploding in complexity, businesses need a graph database that can handle streaming data without burning through cloud budgets. That’s where we come in. 3. What do you love about your team, and why are you the ones to solve this problem? We have a team of engineers obsessed with performance, optimizations, and making complex things simple. No fluff, no bureaucracy, just a relentless focus on building a graph database that’s better than anything on the market. We come from backgrounds in engineering, mathematics, and distributed systems, so we know how to push hardware and algorithms to their limits. 4. If you weren’t building your startup, what would you be doing? I would be either making cocktails on the beach and be a top barmen or be a pilot for one of the commercial aviators. 5. At the moment, how do you measure success? What are your metrics? Active deployments to see who is using us in production, query performance to see how fast we can get, developer adoption, open-source contributions, and seeing more engineers adopting Memgraph and solving their challenges. 6. In a few sentences, what do you offer to whom? We offer a fast, real-time graph database for engineers building fraud detection, recommendation engines, network analysis, and AI-powered applications using Memgraph as a context engine in GraphRAG. If you need to process connected data in milliseconds, we’re your best bet. Whether you’re a startup, a bank, or a research lab, we help you analyze complex relationships without overpaying for slow, legacy graph databases. 7. What’s most exciting about your traction to date? Amazing customers and wild use cases. We’re powering AI, GraphRAG, and real-time context problems at some of the most innovative organizations out there—NASA, Cedars-Sinai, and others who can’t afford slow databases. When top-tier teams in space exploration and healthcare trust Memgraph to crunch their most complex graph problems, you know you’re onto something big. 8. Where do you think your growth will be next year? Next year is all about building on top of what this year is all about - and that is GraphRAG and making life easier for developers building AI with graph technology. We’re going deep on merging graphs, GenAI, and automating the messy parts—like figuring out which search methods and algorithms to run for each question. That’s where our Reasoning Graph comes in. Instead of just storing data, Memgraph will actively help decide how to answer, applying context, constraints, and the right retrieval strategies on the fly. how 9. Tell us about your first paying customer and revenue expectations over the next year. Our first customer is a Swiss company named Saporo. They use graphs to reduce identity attack surface by finding and addressing the most dangerous access (mis)configurations. We have several other customers dealing with cybersecurity and althought last year was very successful for us, as Graph RAG use cases are becoming more popular we anticipate further revenue growth. 10. What’s your biggest threat? Our biggest challenge is also our biggest opportunity—the adoption of graph technology and awareness about your data being inherently interconnected which represents an enormous opportunity. While many organizations are still unfamiliar with graph technology, those who explore it quickly see its transformative power in analyzing complex relationships and making smarter business decisions. This is why education and advocacy are at the heart of what we do. By helping more people understand the value of connected data, we are not just overcoming obstacles—we are shaping the future of data-driven decision-making and empowering businesses to unlock new possibilities. This startup founder interview template is based on HackerNoon Founder & CEO David Smooke’s ten questions for startup founders. This startup founder interview template is based on HackerNoon Founder & CEO David Smooke’s ten questions for startup founders. HackerNoon Founder & CEO David Smooke ten questions for startup founders

This CEO Got Bill Gates’ Attention—Now He’s Fueling AI with Memgraph’s Speedy Graph Tech

Startups of The Year 2023 Winners: Europe

Section 14 - The Production of Ideas

Multimodal AI for High-Fidelity Video Creation and Editing

Tokyo-based Mawari Network has raised $10.8 million in a strategic funding round, positioning the company at the forefront of the rapidly evolving spatial computing industry. The investment, announced on September 26, 2024, was led by Anfield LTD, Borderless Capital, and 1kx, with participation from a diverse group of venture capital firms and angel investors. Mawari, founded in 2017, has developed a decentralized content delivery network (CDN) specifically designed for immersive 3D experiences. The company's technology enables real-time streaming of 3D content to spatial computing devices such as the Apple Vision Pro, Meta Quest 3, and Meta Orion AR Glasses. Luis Oscar Ramirez, Founder & CEO of Mawari, stated, "Our vision has always been to bring immersive experiences to everyone, and this investment will unlock the platform for a broader community to build the 3D Internet with us." The funding round attracted notable investors from both Web2 and Web3 sectors, highlighting the growing interest in spatial computing technologies. Sean Carey, Helium Co-Founder and Partner at Borderless Capital, praised Mawari's innovation, saying, "Every time I see what Mawari is building, I am reminded of how wild the future of spatial computing will be." Mawari's technology consists of two key components: The Spatial Streaming SDK: A toolkit that integrates with popular development environments like Unity and Unreal Engine, allowing creators to focus on content creation without worrying about backend complexities.


The Mawari Network: A decentralized, GPU-powered content delivery network optimized for spatial computing, leveraging a global network of nodes to ensure low latency and high performance. The company has already secured three patents, with 11 more in process, and boasts a client roster of 40 global brands, including T-Mobile, Sapporo, KDDI, Netflix, and BMW. Prior to this funding round, Mawari had been bootstrapped, averaging $1.5 million in annual revenue. Christopher Heymann, Founding Partner at 1kx, noted, "Mawari is not only an early pioneer in spatial computing but is also one of the first of a new cohort of successful Web2 businesses harnessing blockchain and decentralization to drive innovation, efficiency, and improved user experience." The new funds will be used to expand into new markets, enhance the Spatial Streaming SDK, and continue research and development efforts. Mawari also plans to conduct a node license sale in Q4 of 2024 to further decentralize and scale its spatial computing network. As the spatial computing industry continues to grow, Mawari's innovative approach to content delivery and its strong patent portfolio position the company as a key player in shaping the future of immersive digital experiences. Don’t forget to like and share the story! Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program. HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR Tokyo-based Mawari Network has raised $10.8 million in a strategic funding round, positioning the company at the forefront of the rapidly evolving spatial computing industry. The investment, announced on September 26, 2024, was led by Anfield LTD, Borderless Capital, and 1kx, with participation from a diverse group of venture capital firms and angel investors. Mawari, founded in 2017, has developed a decentralized content delivery network (CDN) specifically designed for immersive 3D experiences. The company's technology enables real-time streaming of 3D content to spatial computing devices such as the Apple Vision Pro, Meta Quest 3, and Meta Orion AR Glasses. Luis Oscar Ramirez, Founder & CEO of Mawari, stated, "Our vision has always been to bring immersive experiences to everyone, and this investment will unlock the platform for a broader community to build the 3D Internet with us." The funding round attracted notable investors from both Web2 and Web3 sectors, highlighting the growing interest in spatial computing technologies. Sean Carey, Helium Co-Founder and Partner at Borderless Capital, praised Mawari's innovation, saying, "Every time I see what Mawari is building, I am reminded of how wild the future of spatial computing will be." Mawari's technology consists of two key components: The Spatial Streaming SDK: A toolkit that integrates with popular development environments like Unity and Unreal Engine, allowing creators to focus on content creation without worrying about backend complexities. The Mawari Network: A decentralized, GPU-powered content delivery network optimized for spatial computing, leveraging a global network of nodes to ensure low latency and high performance. The Spatial Streaming SDK: A toolkit that integrates with popular development environments like Unity and Unreal Engine, allowing creators to focus on content creation without worrying about backend complexities. The Spatial Streaming SDK: A toolkit that integrates with popular development environments like Unity and Unreal Engine, allowing creators to focus on content creation without worrying about backend complexities. The Mawari Network: A decentralized, GPU-powered content delivery network optimized for spatial computing, leveraging a global network of nodes to ensure low latency and high performance. The Mawari Network: A decentralized, GPU-powered content delivery network optimized for spatial computing, leveraging a global network of nodes to ensure low latency and high performance. The company has already secured three patents, with 11 more in process, and boasts a client roster of 40 global brands, including T-Mobile, Sapporo, KDDI, Netflix, and BMW. Prior to this funding round, Mawari had been bootstrapped, averaging $1.5 million in annual revenue. Christopher Heymann, Founding Partner at 1kx, noted, "Mawari is not only an early pioneer in spatial computing but is also one of the first of a new cohort of successful Web2 businesses harnessing blockchain and decentralization to drive innovation, efficiency, and improved user experience." The new funds will be used to expand into new markets, enhance the Spatial Streaming SDK, and continue research and development efforts. Mawari also plans to conduct a node license sale in Q4 of 2024 to further decentralize and scale its spatial computing network. As the spatial computing industry continues to grow, Mawari's innovative approach to content delivery and its strong patent portfolio position the company as a key player in shaping the future of immersive digital experiences. Don’t forget to like and share the story! Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program. HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR Vested Interest Disclosure: This author is an independent contributor publishing via our business blogging program . HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR Vested Interest Disclosure: business blogging program business blogging program

Mawari Secures $10.8 Million to Advance Spatial Computing Technology

Мавары забяспечвае 10,8 мільёна долараў на развіццё тэхналогіі прасторавых вылічэнняў

Mawari obtiene 10,8 millones de dólares para impulsar la tecnología de computación espacial

Mawari משיגה 10.8 מיליון דולר לקידום טכנולוגיית מחשוב מרחבית

Mawari osigurava 10,8 milijuna dolara za unaprjeđenje tehnologije prostornog računalstva

Mawari Sekirize $10.8 Milyon Pou Avanse Teknoloji Espasyal Computing

マワリ、空間コンピューティング技術の進歩に向けて1,080万ドルを調達

Мавари орон зайн тооцооллын технологийг хөгжүүлэхийн тулд 10.8 сая долларыг барьцаалж байна

Mawari asigură 10,8 milioane de dolari pentru a promova tehnologia de calcul spațial

ماواری نے مقامی کمپیوٹنگ ٹیکنالوجی کو آگے بڑھانے کے لیے $10.8 ملین کا تحفظ کیا۔

Mavari fazoviy hisoblash texnologiyasini rivojlantirish uchun 10,8 million dollarni kafolatlaydi

Mawari 获 1080 万美元融资，用于推进空间计算技术

Authors:
(1) Edward Crane, School of Mathematics, University of Bristol, BS8 1TH, UK;
(2) Stanislav Volkov, Centre for Mathematical Sciences, Lund University, Box 118 SE-22100, Lund, Sweden. Table of Links Abstract and Introduction Preliminaries Reduction to the case of uniform geometry All original points are eventually removed, a. s. Proof of Theorem 1 Coupling Y (⋅) and Z(⋅) Acknowledgements and References Appendix Acknowledgment The research of S.V. is partially supported by the Swedish Science Foundation grant VR 2019- 04173 and the Crafoord Foundation grant no. 20190667. S.V. would like to acknowledge the hospitality of the University of Bristol during his visits to Bristol. The research of E.C. is supported by the Heilbronn Institute for Mathematical Research. We would like to thank John Mackay for pointing us to the notion of uniform geometry in [7] and Rami Atar for pointing out the relevant Brownian bees model. Finally, we would like to thank the anonymous referee for many useful comments and recommendations, in particular the suggestion to explain what can be done in the non-convex case. References [1] Addario-Berry, Louigi; Lin, Jessica; Tendron, Thomas. Barycentric Brownian bees, Ann. Appl. Probab. 32 (2022), no. 4, 2504–2539. [2] Grinfeld, Michael; Volkov, Stanislav; Wade, Andrew R. Convergence in a multidimensional randomized Keynesian beauty contest, Adv. in Appl. Probab. 47 (2015), no. 1, 57–82. [3] Durrett, Rick. Probability: theory and examples. Fifth edition. Cambridge University Press (2019). [4] Kennerberg, Philip; Volkov, Stanislav. Jante’s law process, Adv. in Appl. Probab. 50 (2018), no. 2, 414–439. [5] Kennerberg, Philip; Volkov, Stanislav. Convergence in the p-contest, Journal of Statistical Physics 178 (2020), 1096–1125. 6] Kennerberg, Philip; Volkov, Stanislav. A Local Barycentric Version of the Bak-Sneppen Model, Journal of Statistical Physics 182:42 (2021), 17 pp. [7] Leonardi, Gian Paolo; Ritor´e, Manuel; Vernadakis, Efstratios. Isoperimetric Inequalities in Unbounded Convex Bodies. Memoirs of the American Math. Soc., no. 1354, Vol. 276 (2022). [8] Siboni, Maor; Sasorov, Pavel and Meerson, Baruch. Fluctuations of a swarm of Brownian bees, Phys. Rev. E 104 (2021), 7 pp. This paper is available on arxiv under CC 4.0 license. Authors: (1) Edward Crane, School of Mathematics, University of Bristol, BS8 1TH, UK; (2) Stanislav Volkov, Centre for Mathematical Sciences, Lund University, Box 118 SE-22100, Lund, Sweden. Authors: Authors: (1) Edward Crane, School of Mathematics, University of Bristol, BS8 1TH, UK; (2) Stanislav Volkov, Centre for Mathematical Sciences, Lund University, Box 118 SE-22100, Lund, Sweden. Table of Links Abstract and Introduction Abstract and Introduction Preliminaries Preliminaries Reduction to the case of uniform geometry Reduction to the case of uniform geometry All original points are eventually removed, a. s. All original points are eventually removed, a. s. Proof of Theorem 1 Proof of Theorem 1 Coupling Y (⋅) and Z(⋅) Coupling Y (⋅) and Z(⋅) Acknowledgements and References Acknowledgements and References Appendix Appendix Acknowledgment The research of S.V. is partially supported by the Swedish Science Foundation grant VR 2019- 04173 and the Crafoord Foundation grant no. 20190667. S.V. would like to acknowledge the hospitality of the University of Bristol during his visits to Bristol. The research of E.C. is supported by the Heilbronn Institute for Mathematical Research. We would like to thank John Mackay for pointing us to the notion of uniform geometry in [7] and Rami Atar for pointing out the relevant Brownian bees model. Finally, we would like to thank the anonymous referee for many useful comments and recommendations, in particular the suggestion to explain what can be done in the non-convex case. References [1] Addario-Berry, Louigi; Lin, Jessica; Tendron, Thomas. Barycentric Brownian bees, Ann. Appl. Probab. 32 (2022), no. 4, 2504–2539. [2] Grinfeld, Michael; Volkov, Stanislav; Wade, Andrew R. Convergence in a multidimensional randomized Keynesian beauty contest, Adv. in Appl. Probab. 47 (2015), no. 1, 57–82. [3] Durrett, Rick. Probability: theory and examples. Fifth edition. Cambridge University Press (2019). [4] Kennerberg, Philip; Volkov, Stanislav. Jante’s law process, Adv. in Appl. Probab. 50 (2018), no. 2, 414–439. [5] Kennerberg, Philip; Volkov, Stanislav. Convergence in the p-contest, Journal of Statistical Physics 178 (2020), 1096–1125. 6] Kennerberg, Philip; Volkov, Stanislav. A Local Barycentric Version of the Bak-Sneppen Model, Journal of Statistical Physics 182:42 (2021), 17 pp. [7] Leonardi, Gian Paolo; Ritor´e, Manuel; Vernadakis, Efstratios. Isoperimetric Inequalities in Unbounded Convex Bodies. Memoirs of the American Math. Soc., no. 1354, Vol. 276 (2022). [8] Siboni, Maor; Sasorov, Pavel and Meerson, Baruch. Fluctuations of a swarm of Brownian bees, Phys. Rev. E 104 (2021), 7 pp. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Analysis of the Jante’s Law Process and Proof of Conjecture: Acknowledgements and References

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions We have investigated whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field coupled to fermions in the RS warped spacetime or not. Imposing CBCs on fields involved in inflation, we have shown that the one-loop effective potential for a Wilson line phase obtained by quantum corrections can behave as an inflaton potential by finding parameter regions consistent with Planck 2018 results. Our model shares basic properties with higher-dimensional models on a flat spacetime, e.g., a potential is generated radiatively, and is robust owing to the gauge symmetry, and then a model has a predictability for physics on inflation. The remaining issues and future prospects are as follows. There is a fine-tuning problem that the (initial) vaules of φ and other parameters should be chosen in order to make φ as an inflaton work well. It would be better if they are determined from a fundamental theory. Or we would have to rely on the anthropic principle in the framework of multiverse. It is necessary to consider contributions of a radion and/or modulus in order to identify an inflaton. In concrete, it is essential to study their stabilization and how inflation can be realized in a system with such several scalar fields including a Wilson line phase on the RS warped background. It would be wonderful to construct a more realistic higher-dimensional gauge theory which solves riddles of particle physics and cosmology on a similar footing. More specifically, it would be fantastic that, in a system governed by the gauge principle, there are several Wilson line phases originated from extra components of gauge bosons, which behave as Higgs boson, an inflaton, a dark matter and so forth. A top-down approach would be useful to construct such a model in a more unified form. Superstring theory, for instance, provides many scalar and vector fields, and possesses many candidates of Higgs boson, an inflaton, a dark matter and so on. Hence, it is intriguing to investigate how a 5d effective theory on the warped geometry can be realized in such a top-down framework. Acknowledgements T.K. would like to thank Dr. O. Seto for the helpful discussions and advice. This work was supported in part by scientific grants from the Ministry of Education, Culture, Sports, Science and Technology under Grant No. 22K03632 (YK). References [1] D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation”, Phys. Rept. 314 , 1 (1999), arXiv:hep-ph/9807278, and references therein. [2] Y. Hosotani, “Dynamical Mass Generation by Compact Extra Dimensions”, Phys. Lett. B126, 309 (1983). [3] Y. Hosotani, “Dynamics of Nonintegrable Phases and Gauge Symmetry Breaking”, Annals. Phys. 190, 233 (1989). [4] N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Extranatural Inflation”, Phys. Rev. Lett. 90, 221302 (2003), arXiv:hep-th/0301218. [5] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Radion stabilization in the presence of a Wilson line phase”, Prog. Theor. Exp. Phys. 2014, 073B04 (2014), arXiv:1404.5125 [hep-th]. [6] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Inflation from radion gauge-Higgs potential at Planck scale”, Prog. Theor. Exp. Phys. 2015, 093B03 (2015), arXiv:1504.06905 [hep-th]. [7] N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters”, Astron. Astrophys. 641, [Erratum: Astron.Astrophys. 652, C4 (2021)], A6 (2020), arXiv:1807.06209 [astro-ph.CO]. [8] L. Randall and R. Sundrum, “A Large mass hierarchy from a small extra dimension”, Phys. Rev. Lett. 83, 3370-3373 (1999), arXiv:hep-ph/9905221. [9] L. Randall and R. Sundrum, “An Alternative to compactification”, Phys. Rev. Lett. 83, 4690-4693 (1999), arXiv:hep-ph/9906064. [10] A. D. Medina, N. R. Shah, and C. E. M. Wagner, “Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions”, Phys. Rev. D 76, 095010 (2007), arXiv:0706.1281 [hep-ph]. [11] Y. Hosotani, K. Oda, T. Ohnuma, and Y. Sakamura, “Dynamical Electroweak Symmetry Breaking in SO(5) × U(1) Gauge-Higgs Unification with Top and Bottom Quarks”, Phys. Rev. D 78, [Erratum: Phys. Rev.D 79, 079902 (2009)], 096002 (2008), arXiv:0806.0480[hep-ph]. [12] Y. Hosotani, “New dimensions from gauge-Higgs unification”, PoS CORFU2016, 026 (2017), arXiv:1702.08161 [hep-ph]. [13] S. Funatsu, H. Hatanaka, Y. Hosotani, Y. Orikasa, and N. Yamatsu, “CKM matrix and FCNC suppression in SO(5)×U(1)×SU(3) gauge-Higgs unification”, Phys. Rev. D 101, 055016 (2020), arXiv:1909.00190 [hep-ph]. [14] A. Hebecker and J. March-Russell, “The structure of GUT breaking by orbifolding”, Nucl. Phys. B 625, 128-150 (2002), arXiv:hep-ph/0107039. [15] N. Haba, Y. Kawamura, and K.-y. Oda, “Dynamical Rearrangement of Theta Parameter in Presence of Mixed Chern-Simons Term”, Phys. Rev. D 78, 085021 (2008), arXiv:0803.4380 [hep-ph]. [16] Y. Abe, Y. Goto, Y. Kawamura, and Y. Nishikawa, “Conjugate boundary condition, hidden particles, and gauge-Higgs inflation”, Mod. Phys. Lett. A 31, 1650208 (2016), arXiv:1608.06393 [hep-ph]. [17] K. Kojima and Y. Okubo, “Early dark energy from a higher-dimensional gauge theory”, Phys. Rev. D 106, 063540 (2022), arXiv:2205.13777 [astro-ph.CO]. [18] C. C´saki, S. Lombardo, and O. Telem, “TASI Lectures on Non-supersymmetric BSM Models”, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics : Anticipating the Next Discoveries in Particle Physics (TASI 2016): Boulder, CO, USA, June 6-July 1, 2016 , edited by R. Essig and I. Low (WSP, 2018), 501-570, arXiv:1811.04279 [hep-ph]. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions We have investigated whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field coupled to fermions in the RS warped spacetime or not. Imposing CBCs on fields involved in inflation, we have shown that the one-loop effective potential for a Wilson line phase obtained by quantum corrections can behave as an inflaton potential by finding parameter regions consistent with Planck 2018 results. Our model shares basic properties with higher-dimensional models on a flat spacetime, e.g., a potential is generated radiatively, and is robust owing to the gauge symmetry, and then a model has a predictability for physics on inflation. The remaining issues and future prospects are as follows. There is a fine-tuning problem that the (initial) vaules of φ and other parameters should be chosen in order to make φ as an inflaton work well. It would be better if they are determined from a fundamental theory. Or we would have to rely on the anthropic principle in the framework of multiverse. It is necessary to consider contributions of a radion and/or modulus in order to identify an inflaton. In concrete, it is essential to study their stabilization and how inflation can be realized in a system with such several scalar fields including a Wilson line phase on the RS warped background. It would be wonderful to construct a more realistic higher-dimensional gauge theory which solves riddles of particle physics and cosmology on a similar footing. More specifically, it would be fantastic that, in a system governed by the gauge principle, there are several Wilson line phases originated from extra components of gauge bosons, which behave as Higgs boson, an inflaton, a dark matter and so forth. A top-down approach would be useful to construct such a model in a more unified form. Superstring theory, for instance, provides many scalar and vector fields, and possesses many candidates of Higgs boson, an inflaton, a dark matter and so on. Hence, it is intriguing to investigate how a 5d effective theory on the warped geometry can be realized in such a top-down framework. Acknowledgements T.K. would like to thank Dr. O. Seto for the helpful discussions and advice. This work was supported in part by scientific grants from the Ministry of Education, Culture, Sports, Science and Technology under Grant No. 22K03632 (YK). References [1] D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation”, Phys. Rept. 314 , 1 (1999), arXiv:hep-ph/9807278, and references therein. [2] Y. Hosotani, “Dynamical Mass Generation by Compact Extra Dimensions”, Phys. Lett. B126, 309 (1983). [3] Y. Hosotani, “Dynamics of Nonintegrable Phases and Gauge Symmetry Breaking”, Annals. Phys. 190, 233 (1989). [4] N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Extranatural Inflation”, Phys. Rev. Lett. 90, 221302 (2003), arXiv:hep-th/0301218. [5] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Radion stabilization in the presence of a Wilson line phase”, Prog. Theor. Exp. Phys. 2014, 073B04 (2014), arXiv:1404.5125 [hep-th]. [6] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Inflation from radion gauge-Higgs potential at Planck scale”, Prog. Theor. Exp. Phys. 2015, 093B03 (2015), arXiv:1504.06905 [hep-th]. [7] N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters”, Astron. Astrophys. 641, [Erratum: Astron.Astrophys. 652, C4 (2021)], A6 (2020), arXiv:1807.06209 [astro-ph.CO]. [8] L. Randall and R. Sundrum, “A Large mass hierarchy from a small extra dimension”, Phys. Rev. Lett. 83, 3370-3373 (1999), arXiv:hep-ph/9905221. [9] L. Randall and R. Sundrum, “An Alternative to compactification”, Phys. Rev. Lett. 83, 4690-4693 (1999), arXiv:hep-ph/9906064. [10] A. D. Medina, N. R. Shah, and C. E. M. Wagner, “Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions”, Phys. Rev. D 76, 095010 (2007), arXiv:0706.1281 [hep-ph]. [11] Y. Hosotani, K. Oda, T. Ohnuma, and Y. Sakamura, “Dynamical Electroweak Symmetry Breaking in SO(5) × U(1) Gauge-Higgs Unification with Top and Bottom Quarks”, Phys. Rev. D 78, [Erratum: Phys. Rev.D 79, 079902 (2009)], 096002 (2008), arXiv:0806.0480[hep-ph]. [12] Y. Hosotani, “New dimensions from gauge-Higgs unification”, PoS CORFU2016, 026 (2017), arXiv:1702.08161 [hep-ph]. [13] S. Funatsu, H. Hatanaka, Y. Hosotani, Y. Orikasa, and N. Yamatsu, “CKM matrix and FCNC suppression in SO(5)×U(1)×SU(3) gauge-Higgs unification”, Phys. Rev. D 101, 055016 (2020), arXiv:1909.00190 [hep-ph]. [14] A. Hebecker and J. March-Russell, “The structure of GUT breaking by orbifolding”, Nucl. Phys. B 625, 128-150 (2002), arXiv:hep-ph/0107039. [15] N. Haba, Y. Kawamura, and K.-y. Oda, “Dynamical Rearrangement of Theta Parameter in Presence of Mixed Chern-Simons Term”, Phys. Rev. D 78, 085021 (2008), arXiv:0803.4380 [hep-ph]. [16] Y. Abe, Y. Goto, Y. Kawamura, and Y. Nishikawa, “Conjugate boundary condition, hidden particles, and gauge-Higgs inflation”, Mod. Phys. Lett. A 31, 1650208 (2016), arXiv:1608.06393 [hep-ph]. [17] K. Kojima and Y. Okubo, “Early dark energy from a higher-dimensional gauge theory”, Phys. Rev. D 106, 063540 (2022), arXiv:2205.13777 [astro-ph.CO]. [18] C. C´saki, S. Lombardo, and O. Telem, “TASI Lectures on Non-supersymmetric BSM Models”, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics : Anticipating the Next Discoveries in Particle Physics (TASI 2016): Boulder, CO, USA, June 6-July 1, 2016 , edited by R. Essig and I. Low (WSP, 2018), 501-570, arXiv:1811.04279 [hep-ph]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Exploring Gauge-Higgs Inflation with Extra Dimensions: Conclusions, Acknowledgements, and References

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 3 Gauge-Higgs inflation on a warped background 3.2 Model with a single fermion A graph of V (φ) is depicted in Figure 1. Here, it is obtained by summing the function 3.3 Model with multiple fermions Next, let us consider a combination of these cos-type potentials. We have now two fermions ψ1 and ψ2. Each fermion has the values of α, β and qψ as shown in Table 2, and then the potential is written as This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References 3 Gauge-Higgs inflation on a warped background 3.2 Model with a single fermion A graph of V (φ) is depicted in Figure 1. Here, it is obtained by summing the function 3.3 Model with multiple fermions Next, let us consider a combination of these cos-type potentials. We have now two fermions ψ1 and ψ2. Each fermion has the values of α, β and qψ as shown in Table 2, and then the potential is written as This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Exploring Gauge-Higgs Inflation with Extra Dimensions: On a Warped Background

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 2 U(1) gauge theory on a warped background 2.1 Randall-Sundrum metric and action integral The spacetime is assumed to be 5d one with the RS metric given by [8, 9] 2.2 Conjugate boundary conditions where β is a constant called a twisted phase, the superscript C denotes a 4d charge conjugation, θC is a real number, and the asterisk means the complex conjugation. Then, the covariant derivatives obey the relations: 2.3 Mass spectrum Then, the action integral is rewritten as 2.4 Effective potential Let us derive the effective potential for the Wilson line phase θ(= θ(x)). Taking the standard procedure, a d-dimensional effective potential involving one degree of freedom at the one-loop level is given b This paper is available on arxiv under CC BY 4.0 DEED license. [3] We introduce both Mψ and cσ′ (y) in a general standpoint, and we will see that cσ′ (y) is forbidden by imposing specific boundary conditions on fields in the next subsection. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References 2 U(1) gauge theory on a warped background 2.1 Randall-Sundrum metric and action integral The spacetime is assumed to be 5d one with the RS metric given by [8, 9] 2.2 Conjugate boundary conditions where β is a constant called a twisted phase, the superscript C denotes a 4d charge conjugation, θC is a real number, and the asterisk means the complex conjugation. Then, the covariant derivatives obey the relations: 2.3 Mass spectrum Then, the action integral is rewritten as 2.4 Effective potential Let us derive the effective potential for the Wilson line phase θ(= θ(x)). Taking the standard procedure, a d-dimensional effective potential involving one degree of freedom at the one-loop level is given b This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv [3] We introduce both Mψ and cσ′ (y) in a general standpoint, and we will see that cσ′ (y) is forbidden by imposing specific boundary conditions on fields in the next subsection.

Exploring Gauge-Higgs Inflation with Extra Dimensions: U(1) Gauge Theory on a Warped Background

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References Abstract We investigate whether inflation in the early universe can be induced by an extra component of a five-dimensional U(1) gauge field in the Randall-Sundrum warped spacetime or not. We show that an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results. In our model, fields involved in inflation obey a different type of boundary condition from that of the visible particles, and a surviving Wilson line phase can play a specific role for physics beyond the standard model. 1 Introduction Inflation can solve both the flatness problem and the horizon problem at the same time and also explain temperature fluctuations of the cosmic microwave background (CMB) [1]. It is therefore almost certain that inflation occurred in the early universe. However, a specific mechanism or an origin of a quanta called “inflaton” is still a mystery. An inflaton is assumed to be a scalar field in typical models, but its potential is, in general, not stable against quantum (gravity) corrections and should be fine-tuned to satisfy constraints of cosmological observations. This problem stems from the fact that radiative corrections on scalar fields cannot be controlled without any assistance of a powerful symmetry. One way to solve this problem is to consider a higher-dimensional gauge theory, and then a Wilson line phase made of an extra component of a gauge field can become an inflaton whose potential can be determined by the gauge principle. In this scenario, a relevant part of potential is obtained as a function of the Wilson line phase radiatively, taking a finite value [2, 3]. Such an inflaton potential is robust owing to the gauge symmetry and its stability can be guaranteed. A famous five-dimensional (5d) model compactified on a circle S 1 has been proposed in the name of extranatural inflation [4]. In a similar setup, a model with both a radion and a Wilson line phase has been constructed, and it is shown that the radion is stabilized [5] and the Wilson line phase can be, in most cases, an inflaton [6]. Recently, constraints on cosmological parameters from various observations have become more stringent and inflation models can be selected more rigorously [7]. It is valuable to reexamine whether an extranatural inflation scenario is still valid today or not, in a wide variety of spacetime. It is known that the Randall-Sundrum (RS) warped spacetime can provide rich properties in phenomenological aspects of particle physics. For instance, RS1 model provides a solution of the hierarchy problem of the standard model [8], RS2 model explains the weakness of gravitational force on the TeV brane because the graviton localizes on the Planck brane [9], and gauge-Higgs unification (GHU) models in the warped spacetime can show promise as physics beyond the standard model (BSM) [10, 11, 12, 13]. Hence, it would be favorable if a riddle in cosmology such as inflation could be solved in the same background. In this paper, we investigate whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field in the warped background or not. In concrete, we examine whether an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results or not. The RS spacetime contains an orbifold S 1/Z2 and a different type of boundary condition called “conjugate boundary condition” can be imposed on fields to survive an extra component of a gauge boson in QED-like models and this enables fields involved in inflation to play a specific role for BSM. This paper is organized as follows. In the next section, we present a 5d U(1) gauge theory on the warped spacetime. In section 3, we study an extranatural inflation scenario on the warped spacetime based on our model. The last section is devoted to conclusions and discussions. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References Abstract We investigate whether inflation in the early universe can be induced by an extra component of a five-dimensional U(1) gauge field in the Randall-Sundrum warped spacetime or not. We show that an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results. In our model, fields involved in inflation obey a different type of boundary condition from that of the visible particles, and a surviving Wilson line phase can play a specific role for physics beyond the standard model. 1 Introduction Inflation can solve both the flatness problem and the horizon problem at the same time and also explain temperature fluctuations of the cosmic microwave background (CMB) [1]. It is therefore almost certain that inflation occurred in the early universe. However, a specific mechanism or an origin of a quanta called “inflaton” is still a mystery. An inflaton is assumed to be a scalar field in typical models, but its potential is, in general, not stable against quantum (gravity) corrections and should be fine-tuned to satisfy constraints of cosmological observations. This problem stems from the fact that radiative corrections on scalar fields cannot be controlled without any assistance of a powerful symmetry. One way to solve this problem is to consider a higher-dimensional gauge theory, and then a Wilson line phase made of an extra component of a gauge field can become an inflaton whose potential can be determined by the gauge principle. In this scenario, a relevant part of potential is obtained as a function of the Wilson line phase radiatively, taking a finite value [2, 3]. Such an inflaton potential is robust owing to the gauge symmetry and its stability can be guaranteed. A famous five-dimensional (5d) model compactified on a circle S 1 has been proposed in the name of extranatural inflation [4]. In a similar setup, a model with both a radion and a Wilson line phase has been constructed, and it is shown that the radion is stabilized [5] and the Wilson line phase can be, in most cases, an inflaton [6]. Recently, constraints on cosmological parameters from various observations have become more stringent and inflation models can be selected more rigorously [7]. It is valuable to reexamine whether an extranatural inflation scenario is still valid today or not, in a wide variety of spacetime. It is known that the Randall-Sundrum (RS) warped spacetime can provide rich properties in phenomenological aspects of particle physics. For instance, RS1 model provides a solution of the hierarchy problem of the standard model [8], RS2 model explains the weakness of gravitational force on the TeV brane because the graviton localizes on the Planck brane [9], and gauge-Higgs unification (GHU) models in the warped spacetime can show promise as physics beyond the standard model (BSM) [10, 11, 12, 13]. Hence, it would be favorable if a riddle in cosmology such as inflation could be solved in the same background. In this paper, we investigate whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field in the warped background or not. In concrete, we examine whether an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results or not. The RS spacetime contains an orbifold S 1/Z2 and a different type of boundary condition called “conjugate boundary condition” can be imposed on fields to survive an extra component of a gauge boson in QED-like models and this enables fields involved in inflation to play a specific role for BSM. This paper is organized as follows. In the next section, we present a 5d U(1) gauge theory on the warped spacetime. In section 3, we study an extranatural inflation scenario on the warped spacetime based on our model. The last section is devoted to conclusions and discussions. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Stories, News & Mentions about SAPORO

Categories

Trending Topics

Stories, News & Mentions about SAPORO

Saporo’s Stories on HackerNoon

Saporo's News & Mentions

Categories

Trending Topics