Supersymmetric Cardy formula and the Weak Gravity Conjecture in AdS/CFT

• Published in: The journal of high energy physics Vol. 2023; no. 11; pp. 118 - 26
• Main Authors: Cho, Minseok, Choi, Sunjin, Lee, Ki-Hong, Song, Jaewon
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 20.11.2023; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes; Classical and Quantum Gravitation; Elementary Particles; Energy; Entropy; Field theory; Gauge theory; Gravity; High energy physics; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scale and Conformal Symmetries; Spacetime; String Theory; Supersymmetric Gauge Theory; Upper bounds; AdS-CFT Correspondence; Scale and Conformal Symmetries; Black Holes; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2023)118

A bstract The Weak Gravity Conjecture (WGC) in anti-de Sitter spacetime (AdS) asserts the existence of an operator in the boundary conformal field theory (CFT) whose scaling dimension-to-charge ratio satisfies a certain upper bound. This bound is specified by the ratio of the conformal central charge c and the flavor central charge k F . We propose a modified bound in AdS 5 /CFT 4 , determined by a combination of two central charges 3 c − 2 a instead of c . This combination arises in the Cardy-like limit of the 4d superconformal index, which captures the Bekenstein-Hawking entropy of large BPS black holes in AdS 5 . Using the new bound, we find that certain superconformal field theories (SCFTs) that are previously thought to violate the AdS WGC, including SQCDs in the conformal window, do satisfy the WGC. We check this version of the WGC against all possible superconformal gauge theories with SU( N ) gauge group admitting a large N limit when the superpotential is absent. We conjecture the modified version of the WGC is a generic property of any 4d SCFT, regardless of the existence of a weakly coupled gravity dual or a large N limit.