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Topics in Quantum Gravity and Field Theory University of California Santa Barbara Topics in Quantum Gravity and Field Theory A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Benjamin Lewis Michel Committee in charge: Professor Joseph Polchinski, Chair Professor Mark Srednicki Professor David Stuart September 2017 The Dissertation of Benjamin Lewis Michel is approved. Professor Mark Srednicki Professor David Stuart Professor Joseph Polchinski, Committee Chair September 2017 Topics in Quantum Gravity and Field Theory Copyright c 2017 by Benjamin Lewis Michel iii To my grandparents: Bob and Joan, Vivi and Herb. iv Acknowledgements If I attempted a proper acknowledgement of everyone who has helped me to this point it would be very long, mostly boring and woefully incomplete. Instead, I will just say that I owe many deep debts of gratitude: to the hep-th community at UCSB and beyond, for wonderful interactions; to my collaborators and co- conspirators, especially my academic siblings; to my cohort, and to old friends; to my family, and to Sarah; to Joe, for some of the most thrilling years of my intellectual life, and to Mark, for his steady wisdom. v Curriculum Vitæ Benjamin Lewis Michel Education 2017 Ph.D. in Physics (Expected), University of California, Santa Barbara. 2014 M.A. in Physics, University of California, Santa Barbara. 2010 A.B. in Physics, Harvard University. Publications F. Chen, B. Michel, J. Polchinski and A. Puhm, Journey to the Center of the • Fuzzball, JHEP 02 (2015) 081 doi:10.1007/JHEP02(2015)081 [arXiv:1408.4798 [hep-th]] B. Michel, E. Mintun, J. Polchinski, A. Puhm and P. Saad, Remarks on brane • and antibrane dynamics, JHEP 1509, 021 (2015) doi:10.1007/JHEP09(2015)021 [arXiv:1412.5702 [hep-th]]. B. Michel, J. Polchinski, V. Rosenhaus and S. J. Suh, Four-point function in • the IOP matrix model, JHEP 1605, 048 (2016) doi:10.1007/JHEP05(2016)048 [arXiv:1602.06422 [hep-th]]. A. Belin, J. de Boer, J. Kruthoff, B. Michel, E. Shaghoulian and M. Shyani, • Universality of sparse d > 2 conformal field theory at large N, JHEP 1703, 067 (2017) doi:10.1007/JHEP03(2017)067 [arXiv:1610.06186 [hep-th]]. W. Donnelly, B. Michel, D. Marolf and J. Wien, Living on the Edge: A Toy • Model for Holographic Reconstruction of Algebras with Centers, JHEP 1704, 093 (2017) doi:10.1007/JHEP04(2017)093 [arXiv:1611.05841 [hep-th]]. W. Donnelly, B. Michel, and A. Wall, Electromagnetic Duality and Entan- • glement Anomalies, Phys. Rev. D96 no. 4 (2017) 045008 10.1103/Phys- RevD.96.045008 [arXiv:1611.0592 [hep-th]]. B. Michel, Remarks on Rindler Quantization, arXiv:1612.03158 [hep-th]. • D. Marolf, B. Michel and A. Puhm, A rough end for smooth microstate ge- • ometries, JHEP 1705, 021 (2017) doi:10.1007/JHEP05(2017)021 [arXiv:1612.05235 [hep-th]]. B. Michel and M. Srednicki, Entanglement Entropy and Boundary Conditions • in 1+1 Dimensions, arXiv:1612.08682 [hep-th]. vi Abstract Topics in Quantum Gravity and Field Theory by Benjamin Lewis Michel This dissertation addresses a variety of open questions in quantum field theory and quantum gravity. The work fits broadly into two categories: attempts to study black holes and brane dynamics in models of quantum gravity, and attempts to study the entangling surface in quantum field theory. vii Contents Curriculum Vitae vi Abstract vii 1 Introduction 1 1.1 Permissions and Attributions . .1 2 Black holes and branes 4 2.1 Introduction . .4 2.2 Journey to the Center of the Fuzzball, and A Rough End for Smooth Microstate Geometries . .8 2.3 Four-point function in the IOP matrix model . 77 2.4 Remarks on brane and antibrane dynamics . 117 2.5 Universality of sparse d > 2 conformal field theory at large N .. 143 3 Entanglement 218 3.1 Introduction . 218 3.2 Entanglement Entropy and Boundary Conditions in 1+1 Dimensions221 3.3 Electromagnetic duality and entanglement anomalies . 243 3.4 Remarks on Rindler Quantization . 287 3.5 Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers . 314 Bibliography 344 viii Chapter 1 Introduction This dissertation studies a number of open problems in quantum gravity and quantum field theory. In quantum gravity the questions largely center around black holes and brane dynamics while in field theory the main focus is entangle- ment entropy, with particular attention to the entangling surface. More details are given in the relevant sections. 1.1 Permissions and Attributions 1. The content of 2.2 is the result of two collaborations: one with Fang x Chen, Joseph Polchinski and Andrea Puhm; the other with Donald Marolf and Andrea Puhm. Both have previously appeared in the Journal of High Energy Physics (JHEP) [57, 319]. They are reproduced here under the terms of the Creative Commons Attribution Noncommercial License: https:// creativecommons.org/licenses/by-nc/3.0/us/. 1 Introduction Chapter 1 2. The content of 2.3 is the result of a collaboration with Joseph Polchinski, x Vladimir Rosenhaus and S. Josephine Suh, and has previously appeared in the Journal of High Energy Physics (JHEP) [315]. It is reproduced here un- der the terms of the Creative Commons Attribution Noncommercial License: https://creativecommons.org/licenses/by-nc/3.0/us/. 3. The content of 2.4 is the result of a collaboration with Eric Mintun, Joseph x Polchinski, Andrea Puhm and Philip Saad, and has previously appeared in the Journal of High Energy Physics (JHEP) [314]. It is reproduced here un- der the terms of the Creative Commons Attribution Noncommercial License: https://creativecommons.org/licenses/by-nc/3.0/us/. 4. The content of 2.5 is the result of a collaboration with Alexandre Belin, x Jan de Boer, Jorrit Kruthoff, Edgar Shaghoulian and Milind Shyani, and has previously appeared in the Journal of High Energy Physics (JHEP) [316]. It is reproduced here under the terms of the Creative Commons Attribu- tion Noncommercial License: https://creativecommons.org/licenses/ by-nc/3.0/us/. 5. The content of 3.2 is the result of a collaboration with Mark Srednicki and x is available as a preprint on arXiv.org [320]. It is reproduced here under the terms of their non-exclusive distribution license: https://arxiv.org/ licenses/nonexclusive-distrib/1.0/license.html. 6. The content of 3.3 is the result of a collaboration with William Donnelly x and Aron C. Wall, and has previously appeared in Phys. Rev. D [222]. It is reproduced here with permission from the publisher, the American Phys- 2 Introduction Chapter 1 ical Society: http://publish.aps.org/copyrightFAQ.html#thesis. See http://forms.aps.org/author/copytrnsfr.pdf for the official copyright transfer agreement. 7. The content of 3.4 is available as a preprint on arXiv.org [318]. It is x reproduced here under the terms of their non-exclusive distribution license: https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html. 8. The content of 3.5 is the result of a collaboration with William Donnelly, x Donald Marolf and Jason Wien, and has previously appeared in the Journal of High Energy Physics (JHEP) [317]. It is reproduced here under the terms of the Creative Commons Attribution Noncommercial License: https:// creativecommons.org/licenses/by-nc/3.0/us/. 3 Chapter 2 Black holes and branes 2.1 Introduction Black holes are objects of central interest in modern physics for reasons nu- merous, varied and deep. Beyond their ubiquity in general relativity and their astrophysical importance (as galactic epicenters [321, 322], sources of detectable gravitational waves [323] and much more [324, 325]) they geometrize a fascinating array of non-gravitational phenomena via holography [327] and, further, manifest the core tension between quantum mechanics and general relativity: the informa- tion paradox [40]. This paradox has recently been the subject of great controversy as its study has lead to new fundamental questions about the of nature black holes { especially, whether their interiors even exist, or if instead spacetime ends violently in a “firewall" near the event horizon [41]. The firewall is a dramatic de- parture from the conventional expectations of general relativity, but its existence is supported by a wide variety of arguments [42, 328]; nonetheless a dynamical 4 Black holes and branes Chapter 2 mechanism for its formation is lacking. Faced with such a conflict between the predictions of quantum mechanics and general relativity, it is natural to look for resolution in string theory, where the two are united. Of course, this approach is nothing new: string theorists have been studying black holes for decades (see [329] for references), prompted by the original information paradox and mysteries about the origins of black hole entropy [45]. Black holes in string theory correspond to bound states of strings and branes [44], providing (in principle) a concrete setting for the study of black hole physics in the full quantum gravity arena. Studies of particularly supersymmetric black holes have even yielded proposals [5] for the realization of the black hole microstates as individual spacetimes, dubbed \fuzzballs", whose aggregate dynamics reproduces the naive black hole geometry of general relativity [30]. Branes are also of general interest as fundamental objects in string theory: they are the extended charges coupling to the p-forms of the massless sector and the objects on which open strings can end [238]; they arise as the duals of ordinary string configurations, and manifest the web of dualities that unifies the different string theories [330, 331]. Apart from black holes they describe a surprising variety of physics: they geometrize field-theoretic phenomena such as confinement [36, 38], the moduli space of vacua in supersymmetric theories [332] and Seiberg- Witten duality [333], and can be used to construct new field theories even in the absence of a Lagrangian description [334]; they naturally give rise both to lower- dimensional subspaces and gauge groups in string compactifications, and their phenomenological applications are broad.
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