Symmetries in Quantum Field Theory and Quantum Gravity
Abstract 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 inconsi...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/136761 |
| _version_ | 1811089759200608256 |
|---|---|
| author | Harlow, Daniel Ooguri, Hirosi |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Harlow, Daniel Ooguri, Hirosi |
| author_sort | Harlow, Daniel |
| collection | MIT |
| description | Abstract
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
$$\pi ^0\rightarrow \gamma \gamma $$
π
0
→
γ
γ
in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in
$$d+1$$
d
+
1
dimensions with horizon topology
$${\mathbb {T}}^p\times {\mathbb {S}}^{d-p-1}$$
T
p
×
S
d
-
p
-
1
. |
| first_indexed | 2024-09-23T14:24:16Z |
| format | Article |
| id | mit-1721.1/136761 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:24:16Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1367612024-01-03T18:04:04Z Symmetries in Quantum Field Theory and Quantum Gravity Harlow, Daniel Ooguri, Hirosi Massachusetts Institute of Technology. Center for Theoretical Physics Abstract 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 $$\pi ^0\rightarrow \gamma \gamma $$ π 0 → γ γ in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in $$d+1$$ d + 1 dimensions with horizon topology $${\mathbb {T}}^p\times {\mathbb {S}}^{d-p-1}$$ T p × S d - p - 1 . 2021-11-01T14:33:10Z 2021-11-01T14:33:10Z 2021-04-05 2021-04-16T03:24:56Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136761 en https://doi.org/10.1007/s00220-021-04040-y Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Harlow, Daniel Ooguri, Hirosi Symmetries in Quantum Field Theory and Quantum Gravity |
| title | Symmetries in Quantum Field Theory and Quantum Gravity |
| title_full | Symmetries in Quantum Field Theory and Quantum Gravity |
| title_fullStr | Symmetries in Quantum Field Theory and Quantum Gravity |
| title_full_unstemmed | Symmetries in Quantum Field Theory and Quantum Gravity |
| title_short | Symmetries in Quantum Field Theory and Quantum Gravity |
| title_sort | symmetries in quantum field theory and quantum gravity |
| url | https://hdl.handle.net/1721.1/136761 |
| work_keys_str_mv | AT harlowdaniel symmetriesinquantumfieldtheoryandquantumgravity AT oogurihirosi symmetriesinquantumfieldtheoryandquantumgravity |