Thermal QCD Phenomenology at Intermediate Gauge/'t Hooft Coupling: Conclusion and Future Outlook

Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract Acknowledgment PART I Chapter 1: Introduction Chapter 2: SU(3) LECs from Type IIA String Theory Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation Chapter 4: Conclusion and Future Outlook PART II Chapter 5: Introduction Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times Chapter 9: Multiverse in Karch-Randall Braneworld Chapter 10: Conclusion and Future outlook APPENDIX A APPENDIX B APPENDIX C Bibliography CHAPTER 10 - CONCLUSION AND FUTURE OUTLOOK In this part of the thesis, we have studied the resolution of information paradox using various proposals, e.g., island proposal, doubly holographic setup, and wedge holography. In this process, we addressed the following issues: • How do the higher derivative terms in the gravitational actions affect the Page curve? • How to obtain the Page curve of black holes with multiple horizons, e.g., Schwarzschild de-Sitter black hole? • Can we describe the “Multiverse” using wedge holography? We started with a very simple example and considered the Reissner Nordström black hole in the presence of O(R2) terms as higher derivative terms, which is a non-holographic model. We considered the two kinds of HD terms: Gauss-Bonnet term and general O(R2) as considered in [141]. Following is the summary of key results obtained in chapter 6 which is based on [10]. • The Page curves of Reissner Nordström black hole are shifting towards later times or earlier times when Gauss-Bonnet coupling (α) increases or decreases. This implies that Page time is being affected due to the presence of HD terms. As soon as islands contribute to the entanglement entropy of Hawking radiation, we get the information from the black hole. Hence, “dominance of islands” in the entanglement entropy of Hawking radiation to compute the Page curve is affected by the higher derivative terms. • We found that scrambling time is affected when we have some other general O(R2) terms, including the Gauss-Bonnet term. In contrast, it is unaffected when we consider only the Gauss-Bonnet term as the higher derivative term. • We showed that our results are consistent with the literature by taking the α → 0 limit. We recover the results of [172] in this limit. We studied the black hole information problem in chapter 8 based on the paper [12] and proposed a method to resolve the information paradox of black holes with multiple horizons. We focused on the Schwarzschild de-Sitter (SdS) black hole, which has two horizons: black hole and de-Sitter horizons. To obtain the Page curve of the black hole, we inserted thermal opaque membranes on both sides so that an observer living on the black hole side can access only the radiation of the black hole patch. We used the island proposal to define the radiation regions in the black hole patch. In this case, gravity is not negligible enough, but one can use the island proposal in the approximation that the observer is very far away from the black hole. Hence, we can use the island proposal. We computed the entanglement entropy of Hawking radiation in the absence and presence of the island surface. After plotting these contributions together, we obtained the Page curve of the black hole patch. We also studied the effect of temperature on the Page curves of black holes. We found that lowtemperature black holes take too much time to deliver the information out of the black holes compared to high-temperature black holes. In the language of entanglement islands, this result is interpreted as follows. “Dominance of islands” and “information recovery” and hence Page time is higher for low-temperature black holes because when islands contribute to the entanglement entropy, we get information from the black hole. In this kind of black hole, it is not possible to obtain the Page curve of the Schwarzschild de-Sitter black hole as a whole due to asymmetrical regions on both sides of the SdS black hole. We constructed the doubly holographic setup from a top-down approach in chapter 7 based on our work [11]. In our setup, the bulk is the eleven-dimensional M-theory uplift inclusive of O(R4) corrections of type IIB string dual constructed in [1]. The external bath to collect the Hawking radiation is a non-conformal thermal QCD bath. We obtained the Page curve of the eternal neutral black hole by computing the entanglement entropies of Hartman-Maldacena and island surfaces in the absence and presence of O(R4) terms. When O(R4) terms are absent, then we obtained the entanglement entropies by computing the areas of extremal surfaces, whereas in the presence of higher derivative terms, we used Dong’s formula to calculate the entanglement entropies. Let us compare the doubly holographic setup constructed from the bottom-up approach and our setup. • Bottom-up double holography with CFT bath: Three descriptions of the doubly holographic setup is given as below. – Boundary Description: d-dimensional BCFT living at AdSd+1-boundary with (d − 1)-dimensional defect. – Intermediate Description: Gravity on d-dimensional end-of-the-world brane coupled to d-dimensional BCFT via transparent boundary condition at the defect. – Bulk Description: d-dimensional BCFT has its own holographic dual which is AdSd+1. • M theory brane description of top-down double holography with QCD bath: Top-down model has three following descriptions similar to the bottom-up model. – Boundary-like Description: QCD2+1 is living at the tip of the conifold i.e. at r = 0. – Intermediate Description: Black M5-brane which contains black hole coupled to QCD2+1 bath living at M2 brane. – Bulk Description: QCD2+1 has holographic dual which is eleven dimensional M theory. Following are the key results that we obtained in chapter 7. • In doubly holographic setups, it was found that one could get the Page curve with massive gravity on the end-of-the-world brane. In our setup, we explicitly showed that this is not the case in the top-down model. We computed the spectrum of graviton on the end-of-the-world brane and found that one could get the Page curve with massless graviton localized on the end-of-the-world brane. • We found that O(R4 ) terms do not affect the Page curve in this setup because contributions to the entanglement entropies are large-N exponentially suppressed. This exponential large-N suppression exists because of massless graviton on the brane. • We showed that no boundary terms arise on the end-of-the-world brane even in the presence of O(R4 ) terms in the bulk, and end-of-the-world brane turns out to be a “fluxed hypersurface” with non-zero tension. • Hartman-Maldacena surface entanglement entropy also exhibits “Swiss-Cheese” structure in large-N scenario. In chapter 9 (which is based on the work done in [13]), we used wedge holography to describe multiverse. The multiverse is constructed as follows. In wedge holography, we have two Karch-Randall branes, and these branes are joined at the defect. The setup is mathematically consistent only if the bulk metric satisfies the Neumann boundary condition (NBC) on the branes. The geometry of the branes can be anti de-Sitter, de-Sitter, or flat space, depending upon the bulk metric. We showed that one can construct a setup of 2n Karch-Randall branes in wedge holography, and the bulk metric still satisfies NBC on the 2n branes. These branes are located at r = ±nρ. We can localize the gravity on these branes using braneworld holography [142, 143]. Therefore, we have 2n branes embedded in the bulk. The geometry of these branes can be anti de-Sitter or de-Sitter or flat space but not the mixture of any two. Hence, we have a multiverse that is made up of 2n gravitating systems. Due to transparent boundary conditions at the defect, various universes existing in the multiverse can communicate with each other. If we consider two multiverses, then there will be the communication of the universes in a specific multiverse but not between the two multiverses. This model applies to the Page curve of black holes with multiple horizons. We explicitly did this for Schwarzschild de-Sitter black hole and argued that we could get the Page curve of the SdS black hole by taking two copies of wedge holography so that one copy describes the Schwarzschild patch with flat space branes and the other copy describes the de-Sitter patch with two de-Sitter branes. By doing so obtained the Page curve of Schwarzschild and de-Sitter patches separately, similar to [12] and concluded that we couldn’t get the Page curve of SdS black hole with two Karch-Randall branes in wedge holography. Since the multiverse consists of communicating universes and hence one could avoid the “grandfather paradox” by not traveling to the universe in which one’s grandfather is living, similar to “many world theory”. Future Outlook: In future, we shall work on the following issues: • Using the doubly holographic setup constructed in chapter 7 from a top-down approach. We will compute the reflected entropy from the bulk point of view [245]. This will shed light on the holographic QCD via gauge-gravity duality. We are interested to see the effect of the O(R4) terms on the reflected entropy and how the higher derivative terms affect the physics of thermal QCD. • We will study the complexity growth of black holes with multiple horizons using the complexity equal volume [246] and complexity equals action proposals [247]. • In chapter 9, we saw that wedge holography is capable of describing the multiverse. The most interesting thing about this setup is that all the universes existing in the multiverse are capable of transferring information with each other. Using this feature, we provided a qualitative resolution of the “grandfather paradox”. We shall work on the more concrete resolution of the “grandfather paradox by providing a quantitative description of the “grandfather paradox” and its resolution. Further, using this setup, we will obtain the Page curve of the Reissner-Nordström de-Sitter black hole. This paper is available on arxiv under CC 4.0 license. Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Authors: Authors: (1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute. Table of Links Abstract Abstract Acknowledgment Acknowledgment PART I PART I Chapter 1: Introduction Chapter 1: Introduction Chapter 2: SU(3) LECs from Type IIA String Theory Chapter 2: SU(3) LECs from Type IIA String Theory Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation Chapter 4: Conclusion and Future Outlook Chapter 4: Conclusion and Future Outlook PART II PART II Chapter 5: Introduction Chapter 5: Introduction Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times Chapter 9: Multiverse in Karch-Randall Braneworld Chapter 9: Multiverse in Karch-Randall Braneworld Chapter 10: Conclusion and Future outlook Chapter 10: Conclusion and Future outlook APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C Bibliography Bibliography CHAPTER 10 - CONCLUSION AND FUTURE OUTLOOK In this part of the thesis, we have studied the resolution of information paradox using various proposals, e.g., island proposal, doubly holographic setup, and wedge holography. In this process, we addressed the following issues: • How do the higher derivative terms in the gravitational actions affect the Page curve? • How to obtain the Page curve of black holes with multiple horizons, e.g., Schwarzschild de-Sitter black hole? • Can we describe the “Multiverse” using wedge holography? We started with a very simple example and considered the Reissner Nordström black hole in the presence of O(R2) terms as higher derivative terms, which is a non-holographic model. We considered the two kinds of HD terms: Gauss-Bonnet term and general O(R2) as considered in [141]. Following is the summary of key results obtained in chapter 6 which is based on [10]. • The Page curves of Reissner Nordström black hole are shifting towards later times or earlier times when Gauss-Bonnet coupling (α) increases or decreases. This implies that Page time is being affected due to the presence of HD terms. As soon as islands contribute to the entanglement entropy of Hawking radiation, we get the information from the black hole. Hence, “dominance of islands” in the entanglement entropy of Hawking radiation to compute the Page curve is affected by the higher derivative terms. • We found that scrambling time is affected when we have some other general O(R2) terms, including the Gauss-Bonnet term. In contrast, it is unaffected when we consider only the Gauss-Bonnet term as the higher derivative term. • We showed that our results are consistent with the literature by taking the α → 0 limit. We recover the results of [172] in this limit. We studied the black hole information problem in chapter 8 based on the paper [12] and proposed a method to resolve the information paradox of black holes with multiple horizons. We focused on the Schwarzschild de-Sitter (SdS) black hole, which has two horizons: black hole and de-Sitter horizons. To obtain the Page curve of the black hole, we inserted thermal opaque membranes on both sides so that an observer living on the black hole side can access only the radiation of the black hole patch. We used the island proposal to define the radiation regions in the black hole patch. In this case, gravity is not negligible enough, but one can use the island proposal in the approximation that the observer is very far away from the black hole. Hence, we can use the island proposal. We computed the entanglement entropy of Hawking radiation in the absence and presence of the island surface. After plotting these contributions together, we obtained the Page curve of the black hole patch. We also studied the effect of temperature on the Page curves of black holes. We found that lowtemperature black holes take too much time to deliver the information out of the black holes compared to high-temperature black holes. In the language of entanglement islands, this result is interpreted as follows. “Dominance of islands” and “information recovery” and hence Page time is higher for low-temperature black holes because when islands contribute to the entanglement entropy, we get information from the black hole. In this kind of black hole, it is not possible to obtain the Page curve of the Schwarzschild de-Sitter black hole as a whole due to asymmetrical regions on both sides of the SdS black hole. We constructed the doubly holographic setup from a top-down approach in chapter 7 based on our work [11]. In our setup, the bulk is the eleven-dimensional M-theory uplift inclusive of O(R4) corrections of type IIB string dual constructed in [1]. The external bath to collect the Hawking radiation is a non-conformal thermal QCD bath. We obtained the Page curve of the eternal neutral black hole by computing the entanglement entropies of Hartman-Maldacena and island surfaces in the absence and presence of O(R4) terms. When O(R4) terms are absent, then we obtained the entanglement entropies by computing the areas of extremal surfaces, whereas in the presence of higher derivative terms, we used Dong’s formula to calculate the entanglement entropies. Let us compare the doubly holographic setup constructed from the bottom-up approach and our setup. • Bottom-up double holography with CFT bath: Three descriptions of the doubly holographic setup is given as below. – Boundary Description: d-dimensional BCFT living at AdSd+1-boundary with (d − 1)-dimensional defect. – Boundary Description: – Intermediate Description: Gravity on d-dimensional end-of-the-world brane coupled to d-dimensional BCFT via transparent boundary condition at the defect. – Intermediate Description: – Bulk Description: d-dimensional BCFT has its own holographic dual which is AdSd+1. – Bulk Description: • M theory brane description of top-down double holography with QCD bath: Top-down model has three following descriptions similar to the bottom-up model. • M theory brane description of top-down double holography with QCD bath: – Boundary-like Description: QCD2+1 is living at the tip of the conifold i.e. at r = 0. – Boundary-like Description: – Intermediate Description: Black M5-brane which contains black hole coupled to QCD2+1 bath living at M2 brane. – Intermediate Description: – Bulk Description: QCD2+1 has holographic dual which is eleven dimensional M theory. – Bulk Description: Following are the key results that we obtained in chapter 7. • In doubly holographic setups, it was found that one could get the Page curve with massive gravity on the end-of-the-world brane. In our setup, we explicitly showed that this is not the case in the top-down model. We computed the spectrum of graviton on the end-of-the-world brane and found that one could get the Page curve with massless graviton localized on the end-of-the-world brane. • We found that O(R4 ) terms do not affect the Page curve in this setup because contributions to the entanglement entropies are large-N exponentially suppressed. This exponential large-N suppression exists because of massless graviton on the brane. • We showed that no boundary terms arise on the end-of-the-world brane even in the presence of O(R4 ) terms in the bulk, and end-of-the-world brane turns out to be a “fluxed hypersurface” with non-zero tension. • Hartman-Maldacena surface entanglement entropy also exhibits “Swiss-Cheese” structure in large-N scenario. In chapter 9 (which is based on the work done in [13]), we used wedge holography to describe multiverse. The multiverse is constructed as follows. In wedge holography, we have two Karch-Randall branes, and these branes are joined at the defect. The setup is mathematically consistent only if the bulk metric satisfies the Neumann boundary condition (NBC) on the branes. The geometry of the branes can be anti de-Sitter, de-Sitter, or flat space, depending upon the bulk metric. We showed that one can construct a setup of 2n Karch-Randall branes in wedge holography, and the bulk metric still satisfies NBC on the 2n branes. These branes are located at r = ±nρ. We can localize the gravity on these branes using braneworld holography [142, 143]. Therefore, we have 2n branes embedded in the bulk. The geometry of these branes can be anti de-Sitter or de-Sitter or flat space but not the mixture of any two. Hence, we have a multiverse that is made up of 2n gravitating systems. Due to transparent boundary conditions at the defect, various universes existing in the multiverse can communicate with each other. If we consider two multiverses, then there will be the communication of the universes in a specific multiverse but not between the two multiverses. This model applies to the Page curve of black holes with multiple horizons. We explicitly did this for Schwarzschild de-Sitter black hole and argued that we could get the Page curve of the SdS black hole by taking two copies of wedge holography so that one copy describes the Schwarzschild patch with flat space branes and the other copy describes the de-Sitter patch with two de-Sitter branes. By doing so obtained the Page curve of Schwarzschild and de-Sitter patches separately, similar to [12] and concluded that we couldn’t get the Page curve of SdS black hole with two Karch-Randall branes in wedge holography. Since the multiverse consists of communicating universes and hence one could avoid the “grandfather paradox” by not traveling to the universe in which one’s grandfather is living, similar to “many world theory”. Future Outlook: In future, we shall work on the following issues: Future Outlook: • Using the doubly holographic setup constructed in chapter 7 from a top-down approach. We will compute the reflected entropy from the bulk point of view [245]. This will shed light on the holographic QCD via gauge-gravity duality. We are interested to see the effect of the O(R4) terms on the reflected entropy and how the higher derivative terms affect the physics of thermal QCD. • We will study the complexity growth of black holes with multiple horizons using the complexity equal volume [246] and complexity equals action proposals [247]. • In chapter 9, we saw that wedge holography is capable of describing the multiverse. The most interesting thing about this setup is that all the universes existing in the multiverse are capable of transferring information with each other. Using this feature, we provided a qualitative resolution of the “grandfather paradox”. We shall work on the more concrete resolution of the “grandfather paradox by providing a quantitative description of the “grandfather paradox” and its resolution. Further, using this setup, we will obtain the Page curve of the Reissner-Nordström de-Sitter black hole. 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