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Title: Universal lowest-twist in CFTs from holography

Abstract

We probe the conformal block structure of a scalar four-point function in d ≥ 2 conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator at large central charge. Such a four-point function can be computed, on the gravity side, as a two-point function of the light operator in a black hole geometry created by the heavy operator. We consider analytically solving the corresponding scalar field equation in a near-boundary expansion and find that the multi-stress tensor conformal blocks are insensitive to the horizon boundary condition. The main result of this paper is that the lowest-twist operator product expansion (OPE) coefficients of the multi-stress tensor conformal blocks are universal: they are fixed by the dimension of the light operators and the ratio between the dimension of the heavy operator and the central charge CT. Neither supersymmetry nor unitary is assumed. Higher-twist coefficients, on the other hand, generally are not protected. A recursion relation allows us to efficiently compute universal lowest-twist coefficients. The universality result hints at the potential existence of a higher-dimensional Virasoro-like symmetry near the lightcone. While we largely focus on the planar black hole limitmore » in this paper, we include some preliminary analysis of the spherical black hole case in an appendix.« less

Authors:
 [1];  [1]
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  1. Boston Univ., MA (United States)
Publication Date:
Research Org.:
Boston Univ., MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1612334
Alternate Identifier(s):
OSTI ID: 1833185
Grant/Contract Number:  
SC0015845
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: 2019; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS; physics; AdS-CFT correspondence; Conformal Field Theory; field theories in higher dimensions

Citation Formats

Fitzpatrick, A. Liam, and Huang, Kuo-Wei. Universal lowest-twist in CFTs from holography. United States: N. p., 2019. Web. doi:10.1007/jhep08(2019)138.
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Fitzpatrick, A. Liam, & Huang, Kuo-Wei. Universal lowest-twist in CFTs from holography. United States. https://doi.org/10.1007/jhep08(2019)138
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Fitzpatrick, A. Liam, and Huang, Kuo-Wei. Mon . "Universal lowest-twist in CFTs from holography". United States. https://doi.org/10.1007/jhep08(2019)138. https://www.osti.gov/servlets/purl/1612334.
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@article{osti_1612334,
title = {Universal lowest-twist in CFTs from holography},
author = {Fitzpatrick, A. Liam and Huang, Kuo-Wei},
abstractNote = {We probe the conformal block structure of a scalar four-point function in d ≥ 2 conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator at large central charge. Such a four-point function can be computed, on the gravity side, as a two-point function of the light operator in a black hole geometry created by the heavy operator. We consider analytically solving the corresponding scalar field equation in a near-boundary expansion and find that the multi-stress tensor conformal blocks are insensitive to the horizon boundary condition. The main result of this paper is that the lowest-twist operator product expansion (OPE) coefficients of the multi-stress tensor conformal blocks are universal: they are fixed by the dimension of the light operators and the ratio between the dimension of the heavy operator and the central charge CT. Neither supersymmetry nor unitary is assumed. Higher-twist coefficients, on the other hand, generally are not protected. A recursion relation allows us to efficiently compute universal lowest-twist coefficients. The universality result hints at the potential existence of a higher-dimensional Virasoro-like symmetry near the lightcone. While we largely focus on the planar black hole limit in this paper, we include some preliminary analysis of the spherical black hole case in an appendix.},
doi = {10.1007/jhep08(2019)138},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2019,
place = {United States},
year = {Mon Aug 26 00:00:00 EDT 2019},
month = {Mon Aug 26 00:00:00 EDT 2019}
}
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https://doi.org/10.1007/jhep08(2019)138
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