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Beyond a = c : gravitational couplings to matter and the stress tensor OPE

Meltzer, David and Perlmutter, Eric (2018) Beyond a = c : gravitational couplings to matter and the stress tensor OPE. Journal of High Energy Physics, 2018 (7). Art. No. 157. ISSN 1126-6708.

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We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large N CFTs with a large gap to single-trace higher spin operators, the stress tensor sector is not only universal, but isolated: that is, ⟨TTO⟩=0, where O≠T is a single-trace primary. We show that this follows from a suppression of ⟨TTO⟩ by powers of the higher spin gap, Δ_(gap), dual to the bulk mass scale of higher spin particles, and explain why ⟨TTO⟩ is a more sensitive probe of Δ_(gap) than a − c in 4d CFTs. This result implies that, on the level of cubic couplings, the existence of a consistent truncation to Einstein gravity is a direct consequence of the absence of higher spins. By proving similar behavior for other couplings ⟨TO_1O_2⟩ where O_i have spin s_i ≤ 2, we are led to propose that 1/Δ_(gap) is the CFT “dual” of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on these three-point couplings that are valid in any CFT. These are generalizations of the Hofman-Maldacena conformal collider bounds. By combining the collider bound on TT couplings to spin-2 operators with analyticity properties of CFT data, we argue that all three tensor structures of 〈TTT〉 in the free-field basis are nonzero in interacting CFTs.

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Additional Information:© 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: January 17, 2018; Accepted: July 10, 2018; Published: July 25, 2018. We thank Clay Cordova, Simone Giombi, Diego Hofman, Petr Kravchuk, Juan Maldacena, Joao Penedones, David Simmons-Duffin, Kostas Skenderis and Joaquin Turiaci for helpful discussions. We also thank Joaquin Turiaci for comments on a draft. We gratefully acknowledge support from Johns Hopkins University during the March Workshop on Quantum Gravity and the Bootstrap, where this work was initiated; from the Simons Summer Workshop at the Simons Center for Geometry and Physics, Stony Brook University; and from the Princeton Center for Theoretical Science. EP is supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671, and by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap). DM is supported by NSF grant PHY-1350180 and Simons Foundation grant 488651.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-91ER40671
Simons Foundation488657
Simons Foundation488651
Subject Keywords:AdS-CFT Correspondence, Conformal Field Theory, Field Theories in Higher Dimensions, Gauge-gravity correspondence
Record Number:CaltechAUTHORS:20180816-133901176
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Official Citation:Meltzer, D. & Perlmutter, E. J. High Energ. Phys. (2018) 2018: 157.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88866
Deposited By: Tony Diaz
Deposited On:16 Aug 2018 21:35
Last Modified:16 Aug 2018 21:35

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