Duality and Supersymmetry Constraints on the Weak Gravity Conjecture

TL;DR

This paper investigates how additional UV symmetries like SL(2,R), O(d,d;R), and supersymmetry influence the validity of the weak gravity conjecture in Einstein-Maxwell-dilaton-axion theories, showing that certain symmetries ensure the conjecture's consistency.

Contribution

It demonstrates that imposing specific UV symmetries can derive the weak gravity conjecture from positivity bounds and null energy conditions, especially when supersymmetry is included.

Findings

SL(2,R) symmetry leads to the weak gravity conjecture via positivity bounds.

O(d,d;R) symmetry imposes a simple condition on Wilson coefficients for positivity.

Supersymmetry causes corrections to vanish, consistent with BPS states.

Abstract

Positivity bounds coming from consistency of UV scattering amplitudes are in general insufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are na\"ively in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved SL($2,\mathbb{R}$) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved O($d,d;\mathbb{R}$) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states.