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 ACKNOWLEDGMENTS I am very grateful to my supervisor, Prof. Aalok Misra, for guiding me during my Ph.D. and making me what I am today. I enjoyed all the discussions that we have together. He trained me so that I can now do independent research. Apart from the research part, I learned many things from him, which helped me in the development of my personality in real life and as a researcher. I am very fortunate to have him as my supervisor. I am very thankful to my supervisor and his family, who always treated me like a family member, and for their encouragement, appreciation, and blessings. Without all these, my Ph.D. journey would not have been so smooth and pleasant. I would like to thank the very humble members of my research committee known as “Student Research Committee (SRC)”: Prof. Tashi Nautiyal (chairperson SRC), Prof. Dibakar Roychowdhury (internal member), Prof. Sugata Gangopadhyay (external member - Department of Computer Science and Engineering, I.I.T. Roorkee) and Prof. Arnab Kundu (Saha Institute of Nuclear Physics (SINP), Kolkata, India, an external member of me as a research fellow of CSIR), for their appreciation, encouragement, valuable comments, questions and evaluating me time to time. I am very grateful to Prof. Dibakar Roychowdhury for the discussions related to the research and post-doctoral position. He always encouraged me not to get tired and never give up. I would like to thank my collaborators, my supervisor, Dr. Vikas Yadav and Mr. Nitin Joshi (Indian Institute of Technology Ropar, Punjab, India) for working on the projects and publishing the papers with me. I would like to thank my colleagues from the string theory and high energy physics group Shivam, Hemant, Jitendra, Salman, Debarshi, Pushpa, Sumit and Abhishek for the valuable discussions, comments and questions. I am very grateful to the two former students from our research group Prof. Pramod Shukla (Bose Institute, Kolkata, India) and Dr. Karunva Sil (University of Cyprus) for their very helpful suggestions and guidance to me which helped me in getting a post-doctoral position. I am very grateful to Prof. Keshav Dasgupta for the help related to academia. I would like to thank Prof. Juan Maldacena (IAS, Princeton, USA), Prof. Andreas Karch (The University of Texas, Austin, USA), Prof. Tadashi Takayanagi (YITP, Kyoto University, Kyoto, Japan), Prof. Kostas Skenderis (University of Southampton, UK), Prof. Thomas Hartman (Cornell University), Prof. Suvrat Raju (ICTS, Bangalore), Prof. David Berenstein (University of California, Santa Barbara, USA), Prof. Xi Dong (University of California, Santa Barbara, USA), Prof. Arpan Bhattacharyya (IIT Gandhinagar, India), Prof. Christoph Uhlemann (University of Oxford), Prof. Rong-Xin Miao (Sun Yat-Sen University, China), Prof. Xuanhua Wang (UCAS, Wenzhou, China), Prof. Xian-Hui Ge (Shanghai University, China), Prof. Mohsen Alishahiha (IPM, Tehran, Iran), Prof. Sanjay Siwach (BHU, India), Prof. Chethan Krishnan (IISc Bangalore) for the useful discussions and comments during my PhD. I would also like to thank Prof. Suresh Tiwari, Prof. Rudra Prakash Malik, and Prof. Bhabani Prasad Mandal from the Banaras Hindu University (BHU), India, who helped me to start my journey into the Theoretical High Energy Physics during my master’s. I would also like to thank the editors, associate editors, and referees of the Journal of High Energy Physics (JHEP), Physical Review D (PRD), Physics Letters B (PLB), and European Physical Journal C (EPJC) for their comments, criticism, etc. Those comments helped me in learning something new which was missing in my papers. I am very grateful to the organizers (including speakers and participants) of the various conferences/workshops/schools for organizing very interesting events. I enjoyed those events and learned about the many new research topics. I would like to thank the members of Indian Physics Association (IPA) Roorkee chapter. I enjoyed working with them. The members include, Prof. Akhilesh Kumar Mishra, Prof. Anjani Kumar Tiwari, Ishani, Aalok, Jaikhomba, Nifeeya, Prem Sagar, Priyanshu, Ritika, Shikha, Tsewang, Vanshaj, Vidisha. I would like to extend my gratitude to all the faculty members, staff, and to students, and postdocs in the Department of Physics at I.I.T. Roorkee for making this a memorable journey. I would like to thank my colleagues from the : Shakti, Soumya, Monika, Amarjyoti, Sonu, Pooja, Pooja, Manish, Veer and Mukesh for bearing me and making the workplace vibrant. I also thank my colleagues from the all the research scholar rooms. I thank my friends Shailesh, Rahul, Anurag, Nandeshwar, Sarvesh, Amit, Ramnivas, Shubhajit for their time to time motivation and encouragement. research scholar room 2 I am very thankful to have wonderful seniors who treated me like younger brother: Shubham, Naveen, Aalok, Dibyendu. I specially thank Prem Sagar who took care of me always during my stay at IIT Roorkee and Deepak for the wonderful company. I would like to thank Priyanka, Pooja and Jaikhomba who helped in various way during pre-synopsis and thesis submission. I am very thankful to Anil, Ramashish, Amarjyoti, Shakti and Soumya for their real life knowledge, I feel everyone should have friends like them but please don’t follow them otherwise you may get bitten at some places. I am also thankful to Shivam and Shubranshu for their valuable time and discussion on the real life issues. It was a great pleasure to have Manish, Brij Mohan, Ashutosh, Arun, Harsh, Ishitwa, Shakti at IIT Roorkee who are the alumni from BHU. I thank my friends Divya, Pavneet, Ankur, Anshu, Hemant, Anju, Rahul, Ashish, Tejaswini, Gagan, Uwais for their valuable time and discussions (on various topics) during my stay at IITR. I am very grateful to my family for their continuous support and everything. I am very grateful to my parents (Shri Shyam Narayan Yadav and Shrimati Chinta Devi) who always left me free to do what I wanted to do. I was very fortunate to learn many things about life from my grandfather (Late Shri Ghurfekan Yadav). Seeing me as “Dr. Gopal Yadav” was his dream, I think he will be very happy for me wherever he will be now. I thank my maternal uncle and aunty, “Phupha” and “Bua”, and brother in laws who always encouraged me to believe in myself and for their support. I am very fortunate to have bhaiya and bhabhi, Rinki di, Priyanka di, Shaloo, Prity, Sandip, Arvind bhaiya, Santosh bhaiya, Ravi bhaiya, Bunty, Aman, Aditya, Mahesh, Vipul, Pooja, Ranjita di, Anjali, Akriti, Ankita, Shrija, Devansh, Shreya, Shivansh, Tejas in my life. I am very grateful to my school teachers, college/university professors, and all of my gurus in various fields for educating me in various aspects of life. Education can bring changes and what I am today is the perfect example of it. This paper is under CC 4.0 license. available on arxiv

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