Beyond a = c : gravitational couplings to matter and the stress tensor OPE
Abstract
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, Δgap, dual to the bulk mass scale of higher spin particles, and explain why < TTO > is a more sensitive probe of Δgap 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 < TO1O2 > where Oi have spin si ≤ 2, we are led to propose that 1/Δgap 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 samemore »
- Authors:
-
- Yale Univ., New Haven, CT (United States). Dept. of Physics
- Princeton Univ., Princeton, NJ (United States). Dept. of Physics; California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1507576
- Grant/Contract Number:
- FG02-91ER40671; 488657; PHY-1350180; 488651
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal Field Theory; Field Theories in Higher Dimensions; Gauge-gravity correspondence
Citation Formats
Meltzer, David, and Perlmutter, Eric. Beyond a = c : gravitational couplings to matter and the stress tensor OPE. United States: N. p., 2018.
Web. doi:10.1007/jhep07(2018)157.
Meltzer, David, & Perlmutter, Eric. Beyond a = c : gravitational couplings to matter and the stress tensor OPE. United States. https://doi.org/10.1007/jhep07(2018)157
Meltzer, David, and Perlmutter, Eric. Wed .
"Beyond a = c : gravitational couplings to matter and the stress tensor OPE". United States. https://doi.org/10.1007/jhep07(2018)157. https://www.osti.gov/servlets/purl/1507576.
@article{osti_1507576,
title = {Beyond a = c : gravitational couplings to matter and the stress tensor OPE},
author = {Meltzer, David and Perlmutter, Eric},
abstractNote = {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, Δgap, dual to the bulk mass scale of higher spin particles, and explain why < TTO > is a more sensitive probe of Δgap 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 < TO1O2 > where Oi have spin si ≤ 2, we are led to propose that 1/Δgap 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.},
doi = {10.1007/jhep07(2018)157},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2018,
place = {United States},
year = {Wed Jul 25 00:00:00 EDT 2018},
month = {Wed Jul 25 00:00:00 EDT 2018}
}
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