City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 2-2014 Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes Debajyoti Sarkar Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/107 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes by Debajyoti Sarkar A dissertation submitted to the Graduate Faculty in Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2014 c 2014 Debajyoti Sarkar All rights reserved ii This manuscript has been read and accepted for the Graduate Faculty in Physics in satisfaction of the dissertation requirement for the degree of Doctor of Philosophy. Date Prof. Daniel N. Kabat Chair of Examining Committee Date Prof. Steven Greenbaum Executive Officer Prof. Dimitra Karabali Prof. V. Parameswaran Nair Prof. Alexios Polychronakos Prof. Martin Schaden Supervisory Committee THE CITY UNIVERSITY OF NEW YORK iii Abstract Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes by Debajyoti Sarkar Advisor: Daniel N. Kabat, Professor of Physics The aim of this dissertation is threefold. We begin by the study of two parallel ideal cosmic strings in the presence of non-minimal scalar fields and spin-1 gauge fields. We show that the contributions of the non-minimal term on the interaction energy between the strings are similar to that of the gauge field for a particular value of non-minimal coupling parameter. In this context we clarify some of the issues that arise when comparing the renormalization of black hole entropy and entanglement entropy using the replica trick. In the second part of the dissertation we study the process of bound state formation in clusters of Dp- brane collision and Dp shell/ Membrane collapse processes. We consider two mechanisms for bound state formation. The first, operative at weak coupling in the worldvolume gauge theory, is creation of W-bosons. The second, operative at strong coupling, corresponds to formation of a black hole in the dual supergravity. These two processes agree qualitatively at intermediate coupling, in accord with the correspondence principle of Horowitz and Polchinski. We show that the size of the bound state and timescale for formation of a bound state agree at the correspondence point, along with other relevant thermodynamic quantities. The timescale involves matching a parametric resonance in the gauge theory to a quasinormal mode in supergravity. Finally we study construction of local operators in AdS using the generalized AdS/ CFT corre- spondence. After briefly sketching previous works on this topic which involve massless and massive iv scalar fields, we present similar construction for spin- 1 and spin- 2 gauge fields. Working in holo- graphic gauge in the bulk, at leading order in 1=N bulk gauge fields are obtained by smearing boundary currents over a sphere on the complexified boundary, while linearized metric fluctuations are obtained by smearing the boundary stress tensor over a ball. This representation respects AdS covariance up to a compensating gauge transformation. We also consider massive vector fields, where the bulk field is obtained by smearing a non-conserved current. We compute bulk two-point functions and show that bulk locality is respected. We show how to include interactions of massive vectors using 1=N perturbation theory, and we comment on the issue of general backgrounds. We point out some more recent works on interacting scalar and gauge fields and try to answer the question of what should be the CFT properties to have a dual gravitational descriptions on AdS space. We end with some speculations about finite N and when we have black holes in the bulk. v To My Family vi Acknowledgments On one hand, it is quite impossible for me to properly acknowledge everyone who have contributed to my academic life and stayed beside me leading to my PhD degree and on the other hand it is a pure pleasure. Especially, I think of myself as being exceptionally lucky to be alongside of so many great people and being fortunate enough to have them sometimes as my friend and sometimes as my guide. But being lucky has its own cost: the list is humongous and they come in so many colors and flavors. So without even trying, I will be very precise and will only name those (unsuccessfully) who have been directly involved and have tremendous effect in my academic world leading to my PhD degree. To begin with, of course I should recall my adviser Prof. Daniel Kabat, a fantastic person, who has shared his knowledge and insights to let me and make me mature in physics and paved my way for the future. Once again there are so many things I can say about him, that I will simply stop. Physics-maturity-wise, he shaped me to who I am, with all the defects being entirely my shortcomings. I would also like to thank him for various financial supports which enabled me to participate in various academic frontiers, which was essential towards my graduation. Among the other faculties at City University of New York (CUNY), I should of course mention Prof. Dimitra Karabali, Prof. V. Parameswaran Nair, Prof. Alexios Polychronakos for not only creating a vibrant research atmosphere at City College/ Lehman College, but also for teaching me various courses and finally serving as my thesis committee member. I would also like to thank Prof. Martin Schaden and Prof. Alberto Nicolis for serving respectively at my thesis and pre-thesis defense committee. Special thanks also goes to Prof. Peter Orland for couple of his fabulous QFT classes and his various advice. And finally among the CUNY faculties, I will end with Prof. Justin Vazquez-Poritz. What vii a wonderful friend, philosopher and guide he has been to me! I will not try to enumerate his contributions because I can’t, but will simply acknowledge that I will always regard him as one of the best mentors that I had at CUNY. I would also like to thank all the CUNY academic and administrative staffs, all the CUNY and outside professors, postdocs and graduate students whom I met at CUNY and elsewhere for helping me out, for sharing their knowledge and for easing my way out. Special thanks goes to Shubho Roy, a postdoc in our group for a couple of years with whom I shared many cups of coffee and learned a lot of things. I would also like to thank Diptarka Das, Norihiro Iizuka, Gilad Lifschytz and Xiao Xiao for past and ongoing collaborations. Special thanks also goes to Mr. Daniel Moy, our Physics APO for many interesting conversations and buckets of help. Personally (and also pre-graduate study wise), I would like to start off with my parents and stop right there. No thesis is long enough to fully reflect their contributions to my life. What about my wife and her family? No. I will have to stop again. May be I will simply say that I am grateful to her for her love and life (and also so that she smiles a bit more if she reads this acknowledgement). Then if I am to name friends starting with most recent ones, in my graduate life all names will be after Dario Capasso. Thanks for being such a great friend! Also during my undergraduate and Masters studies, I have had the fortune of having great friends and teachers. Among my friends, Nirupam Dutta for motivating me towards high energy physics and introducing me to Rajsekhar Bhattacharyya, a wonderful teacher that I had in my college days. And there are Arindam, Debmalya, two Partha’s, Soma, Arko . simply so many. Among the teachers Prof. Babul Dutta, Prof. Partha Pratim Basu and again so many; and then again in my school life I had some of my greatest class mates and teachers who offered me a very competitive and intelligent environment to grew up with. The acknowledgment is already nearly two page long now and I am having a feeling of dissatis- faction mixed with satisfaction and nostalgia. But the submission date is near and may be I should simply conclude by saying: “thanks to you all!” viii Contents Abstract iv Acknowledgments vii 1 Introduction 1 2 Cosmic String Interactions Induced by Gauge and Scalar Fields 5 2.1 Non-minimal scalar energy . .8 2.2 Gauge field energy . 11 2.3 Conclusions . 13 3 Black Hole Formation at the Correspondence Point: Part I 16 3.1 Introduction and summary . 16 3.2 Bound state formation in 0-brane collisions . 18 3.2.1 Perturbative string production . 19 3.2.2 Bound state formation in gravity . 20 3.2.3 Correspondence point . 21 3.3 Dp-brane collisions . 22 3.4 Parametric resonance in perturbative SYM . 24 3.5 Comparison of timescales . 28 3.5.1 0-brane parametric resonance . 28 3.5.2 p-brane parametric resonance . 29 3.5.3 Comparison to quasinormal modes . 30 3.6 Comparison to equilibrium properties . 31 ix 3.7 Shell Collapse . 33 3.8 Conclusions . 37 4 Black Hole Formation at the Correspondence Point: Part II 39 4.1 Introduction . 39 4.2 Fuzzy spheres . 40 4.3 Perturbative sphere collapse . 44 4.4 Black hole formation and the correspondence point . 45 4.5 Back-reaction and parametric resonance . 47 4.6 More on the correspondence point .