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

TL;DR

This paper proposes a modified Weak Gravity Conjecture bound in AdS/CFT, derived from the superconformal index, which resolves previous violations by certain SCFTs and suggests a universal property of 4d SCFTs.

Contribution

It introduces a new bound based on the combination 3c-2a in the superconformal index, extending the WGC applicability to all 4d SCFTs.

Findings

The modified bound is satisfied by SCFTs previously thought to violate WGC.

The new bound aligns with the entropy of large BPS black holes in AdS5.

The conjecture applies universally to 4d SCFTs, independent of gravity duals.

Abstract

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 AdS5/CFT4, determined by a combination of two central charges $3c-2a$ 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 AdS5. 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.