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Symmetries in Quantum Field Theory and Quantum Gravity

Harlow, Daniel and Ooguri, Hirosi (2021) Symmetries in Quantum Field Theory and Quantum Gravity. Communications in Mathematical Physics, 383 (3). pp. 1669-1804. ISSN 0010-3616. doi:10.1007/s00220-021-04040-y.

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In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any “long-range” bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the “convex hull condition” of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and ’t Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman–Mandula theorem to discrete symmetries, and an improved explanation of the decay π⁰→γγ in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in d+1 dimensions with horizon topology T^p×S^(d−p−1).

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Harlow, Daniel0000-0002-1005-4745
Ooguri, Hirosi0000-0001-6021-3778
Additional Information:© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. Received 22 November 2019; Accepted 12 February 2021; Published 05 April 2021. We thank Tom Banks, Thomas Dumitrescu, Zohar Komargodski, Nati Seiberg, and Sasha Zhiboedov for many useful discussions on the issues in this paper. We also thank Nima Arkani-Hamed, Chris Beem, Mu-Chun Chen, Clay Cordova, Simeon Hellerman, Gary Horowitz, Ethan Lake, Hong Liu, Roberto Longo, Juan Maldacena, Greg Moore, Andy Strominger, Raman Sundrum, Wati Taylor, and Edward Witten for useful discussions. We thank the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1607611, the Harvard Center for the Fundamental Laws of Nature, the Institute for Advanced Study, the Kavli Institute for Theoretical Physics, the Okinawa Institute of Science and Technology Graduate School, the Perimeter Institute, the Simons Center for Geometry and Physics, the Yukawa Institute of Fundamental Physics, for their hospitality during various stages of this work. DH also thanks the Kavli Institute for Physics and Mathematics of the Universe and the Maryland Center for Fundamental Physics for hospitality, and Alexander Huabo Yu Harlow for creating a stimulating environment while this work was being completed. DH is supported by the US Department of Energy Grants DE-SC0018944 and DE-SC0019127, the Simons foundation as a member of the It from Qubit collaboration, and the MIT department of physics. HO is supported in part by U.S. Department of Energy Grant DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Harvard UniversityUNSPECIFIED
Institute for Advanced StudyUNSPECIFIED
Kavli Institute for Theoretical PhysicsUNSPECIFIED
Okinawa Institute of Science and TechnologyUNSPECIFIED
Perimeter InstituteUNSPECIFIED
Simons Center for Geometry and PhysicsUNSPECIFIED
Yukawa Institute of Fundamental PhysicsUNSPECIFIED
Department of Energy (DOE)DE-SC0018944
Department of Energy (DOE)DE-SC0019127
Simons FoundationUNSPECIFIED
Massachusetts Institute of Technology (MIT)UNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Japan Society for the Promotion of Science (JSPS)C-26400240
Japan Society for the Promotion of Science (JSPS)15H05895
Issue or Number:3
Record Number:CaltechAUTHORS:20210406-085746056
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Official Citation:Harlow, D., Ooguri, H. Symmetries in Quantum Field Theory and Quantum Gravity. Commun. Math. Phys. 383, 1669–1804 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108630
Deposited By: Tony Diaz
Deposited On:07 Apr 2021 23:49
Last Modified:16 Apr 2021 16:34

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