Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs
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Springer
Received: July 27, 2020 Accepted: October 6, 2020 Published: November 12, 2020
A. Liam Fitzpatrick,a Kuo-Wei Huang,a David Meltzer,b Eric Perlmutterb and David Simmons-Duffinb a
Department of Physics, Boston University, Commonwealth Avenue, Boston, MA 02215, U.S.A. b Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge CT , we clarify the properties of stress tensor composite primary operators of minimal twist, [T m ], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling hOL OL [T m ]i, where OL is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling hT T OL i, the three-point coupling hOL OL [T 2 ]i is modified at large √ CT if hT T OL i ∼ CT . This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to OL can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-` ≥ 2 bulk field at tree level, or any spin ` at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively. Keywords: AdS-CFT Correspondence, Conformal Field Theory, Field Theories in Higher Dimensions ArXiv ePrint: 2007.07382
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)060
JHEP11(2020)060
Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs
Contents 1 Introduction
1
2 Higher-curvature interactions at large CT 2.1 Neutral vs. charged scalar 2.2 Large CT and gravitational scaling
4 5 5 8 8 10 12
4 Local interactions 4.1 Preliminaries 4.2 Explicit OPE coefficients of T 2 4.3 An all-order analysis via a planar black hole
14 15 17 19
5 Discussion
21
A Spinning blocks
22
B Comments on loops
24
1
Introduction
Much of physics is concerned with finding the simplest description possible that nevertheless captures some universal behavior of interest. Ideally, such descriptions can be systematically improved. Effective field theories, and the emergent universality at low energies that they describe, provide a robust instance of this approach. Holographic descriptions of strongly coupled physics, through the AdS/CFT correspondence [1–3], may be cleanly derived as applications of effective field theory in the bulk, provided there exists a certain separation of scales. Such conditions hold i
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