# Weak Gravity Conjecture, Black Hole Entropy, and Modular Invariance

Research paper by Lars Aalsma, Alex Cole, Gary Shiu

Indexed on: 21 Nov '19Published on: 16 May '19Published in: arXiv - High Energy Physics - Theory

#### Abstract

In recent literature, it has been argued that a mild form of the Weak Gravity Conjecture (WGC) is satisfied by wide classes of effective field theories in which higher-derivative corrections can be shown to shift the charge-to-mass ratios of extremal black holes to larger values. However, this mild form does not directly constrain low-energy physics because the black holes satisfying the WGC have masses above the cutoff of the effective theory. In this note, we point out that in string theory modular invariance can connect a light superextremal state to heavy superextremal states; the latter collapse into black holes at small string coupling. In the context of heterotic string theory, we show that these states are black holes that have $\alpha'$-exact charge-to-mass ratios exceeding the classical extremality bound. This suggests that modular invariance of the string partition function can be used to bring the mild form of the WGC to a stronger form.