University of California Santa Barbara Thermal Behavior of Holographic Quantum Field Theories A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Eric Mefford Committee in charge: Professor Gary T. Horowitz, Chair Professor David Berenstein Professor David Weld June 2018 The Dissertation of Eric Mefford is approved. Professor David Berenstein Professor David Weld Professor Gary T. Horowitz, Committee Chair June 2018 Thermal Behavior of Holographic Quantum Field Theories Copyright c 2018 by Eric Mefford iii To Chili iv Acknowledgements First, I would like to thank my advisor Gary Horowitz for his support and mentor- ship during my graduate career. Throughout my time at UCSB, Gary has consistently encouraged me to become a strong independent scientist. This has served his previous students well (congratulations, Netta, on your new faculty position!) and has made me feel very proud of my work. This is best illustrated in my first two papers where, when it came time to publish, he insisted being listed second against convention [1] or that I should publish the paper myself [2]. Finally, he helped fund trips to TASI in Boulder, GR21 in New York, and a workshop in Benasque, Spain, so that I could meet and collaborate with other researchers in the field. I hope one day to be as good a teacher and advisor as he has been to me. Second, I would like to thank Professors Don Marolf and Joe Polchinski. Don has been both a collaborator, a string theory teacher, and a useful resource in my endless confusion with entanglement entropies. Joe was a wonderful mentor and teacher who inspired me and the entire physics community. In addition, he served on my advancement committee and helped organize the TASI summer school in Boulder. I would also like to thank Professors Kengo Maeda and Akihiro Ishibashi, whose visit to Santa Barbara started an exciting set of collaborations which have continued since our first project. They are wonderful collaborators who have taught me how to be respectful and encouraging even when the graduate student on the collaboration (me) is wrong. I would also like to thank David Berenstein and David Weld for serving on my committee. Next, I would like to thank Edgar Shaghoulian. Edgar has been a mentor for me in physics longer than anyone else. At Stanford, he was my TA in junior year, helped v oversee my undergraduate thesis the next summer, and we were co-TA's my senior year. My first year of grad school, he spent a few months at UCSB during the great firewall debates of 2012-2013 and the next year, came to UCSB as a post-doc. We finally found a way to collaborate during his last year here. He has always been a good friend, advisor, and collaborator and while it is at times frustrating, his constant assumption that I am wrong forces me to be a better scientist and explain things in clearer, more concise terms. I would like to thank many graduate students who have been friends and mentors during my time at UCSB. I would first like to thank Kevin Kuns. He and I spent many hours teaching ourselves group theory, tetrad formalism, and the renormalization group to answer problem sets in our first year courses. Kevin has been a great housemate and friend and is my go-to resource for quantum field theory and LIGO and the reliable source for finding good Indian food. I would like to thank Benson Way, Gavin Hartnett, and Netta Engelhardt, for leading the way for me as Gary's previous students and for teaching me numerics and much of what I know about General Relativity. I would like to thank Alex Miller for her friendship and for her amazing ability to become friends with new physicists and to let me tag along. I would like to thank Milind Shyani for being my backup resource for QFT, for being a hilarious person whose never-ending happiness inspires me to never take things too seriously, but mostly for the new gray hairs I grew in the days leading up to our paper submission. Finally, I could not have done this without my friends and family. Jason Iaconis, Andrew Dunsworth, Scott Haselschwardt, and Nick Noll shared my passion for surfing and helped keep me sane during my graduate career. I must thank Bishnu and vi Bhaskar making the day to day tasks of Naomi and my lives easier during the last couple of years. My parents Ivan and Ruth, brothers Tyler and Eric, sisters Caitlin and Melissa have always been there for me especially during some of the more trying times over the last few years and I could not have done this without them. Finally, there are not enough thanks in the world that I can give to Naomi. She is my inspiration and the most caring, strongest person I know. vii Curriculum Vitæ Eric Mefford Education 2018 Ph.D. in Physics (Expected), University of California, Santa Barbara. 2015 M.A. in Physics, University of California, Santa Barbara. 2012 B.Sc. in Physics with Honors and Distinction, Stanford Univer- sity Publications \Sparseness bounds on local operators in holographic CFTd" E. Mefford, E. Shaghoulian, M. Shyani [arXiv:1711.03122] \Holographic stress-energy tensor near the Cauchy horizon inside a ro- tating black hole" A. Ishibashi, K. Maeda, E. Mefford Phys. Rev. D 96 024005 (2017) [arXiv: 1703.09743 [hep-th]] \Time-independent wormholes" Z. Fu, D. Marolf, E. Mefford JHEP 1612, 021 (2016) [arXiv: 1610.08069 [hep-th]] \Entanglement Entropy in Jammed CFTs" E. Mefford JHEP 1709, 006 (2017) [arXiv:1605.09369 [hep-th]] \Simple holographic insulator" E. Mefford and G.T. Horowitz Phys. Rev. D 90 084042, (2014) viii Abstract Thermal Behavior of Holographic Quantum Field Theories by Eric Mefford This dissertation investigates thermal holographic quantum field theories dual to gravitational systems with black holes. This study has relevance for experimental physics in a lab or near an astrophysical black hole as well as for the structure of higher dimensional quantum field theories. The dissertation begins with an introduction to AdS/CFT, entanglement entropy, and numerical methods. The next two chapters explore constraints on holographic quantum field theories with a semi-classical dual. In chapter two, a scalar field is used to construct an \extended wormhole" that connects two identical asymptotic regions and is globally static. Mutual information of identical regions in the two boundary CFTs show that the expanded throat corresponds to rapid thermalization in the field theory. In the third chapter, a finite temperature phase transition in the gravitational path integral is used to constrain the spectrum of charged, spinning operators in the dual thermal CFT. The fourth and fifth chapters are concerned with the study of thermal quantum field theories around black holes. In chapter four, the holographic dual of a zero- temperature quantum field theory on a finite temperature Reissner-Nordstr¨omblack hole background is constructed. The entanglement entropy of annular regions in the field theory explains a phenomenon called \jamming," in which heat flow is impeded ix due to strong interactions. In chapter five, the holographic dual to a quantum field theory on the interior of a doubly-spinning Myers-Perry black hole is constructed. The null energy along the Cauchy horizon diverges negatively, indicating singular behavior and providing evidence for strong cosmic censorship. The sixth chapter constructs the holographic dual to a strongly interacting metal with charged bosonic excitations. Such a field theory is a candidate system to de- scribe the pseudogap phase of the high temperature superconductors. Experiments on these systems exhibit a metal-insulator transition at zero temperature and power- law conductivities at low temperature. On the gravity side, a domain wall potential for a scalar field interpolates between UV and IR conformally invariant spacetimes with different length scales. The dimension of the scalar controls the temperature and frequency dependence of the low temperature conductivity. x Contents Curriculum Vitae viii Abstract ix 1 Introduction 1 1.1 AdS/CFT basics . .7 1.2 Entanglement Entropy . 23 1.3 Numerics . 38 1.4 Permissions and Attributions . 51 2 Time-independent wormholes 53 2.1 Introduction . 53 2.2 Thin Wall Solutions . 55 2.3 Smooth Solutions . 63 2.4 Discussion . 72 2.5 Acknowledgements . 75 2.6 Appendix: No solutions with smooth scalar potentials . 75 3 Sparseness bounds on local operators in holographic CFTd 79 3.1 Introduction . 79 3.2 Method for obtaining bounds . 84 3.3 Bounds on operators . 88 3.4 BPS, cosmic censorship, and sparseness bounds . 110 3.5 Comments on the high-lying spectrum . 114 3.6 Conclusion . 118 3.7 Appendix A: Black hole entropy from deconfining phase transitions . 120 3.8 Appendix B: AdS5, AdS6, and AdS7 details . 121 xi 4 Entanglement entropy in jammed CFTs 134 4.1 Introduction . 134 4.2 Quantum Stress Tensors in Spherically Symmetric Static Spacetimes . 142 4.3 Numerical Construction of RN Boundary Black Holes . 147 4.4 Boundary Stress Tensor . 155 4.5 Entanglement Entropies of Droplets . 164 4.6 Discussion . 185 4.7 Acknowledgments . 187 4.8 Appendix: Stress Tensor Expansion . 187 5 Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole 201 5.1 Introduction . 201 5.2 Derivative expansion method . 205 5.3 The holographic stress-energy tensor . 214 5.4 Numerical results . 218 5.5 Conclusion and discussions . 231 5.6 Acknowledgments . 233 5.7 Appendix: P(r), S(r), R(r), and Q(r)................. 234 6 Simple holographic insulator 238 6.1 Introduction . 238 6.2 The Model . 241 6.3 Conductivity .