Weak Gravity Bounds in Asymptotic String Compactifications

TL;DR

This paper derives a universal asymptotic charge-to-mass ratio formula for BPS states in certain string compactifications, establishing bounds related to the Weak Gravity Conjecture and Swampland criteria.

Contribution

It introduces a formula for asymptotic charge-to-mass ratios in Type IIB Calabi-Yau compactifications using asymptotic Hodge theory, linking to swampland conjectures.

Findings

Derived a universal charge-to-mass ratio formula for asymptotic limits.

Determined extremality bounds for electric BPS black holes.

Connected these bounds to the Weak Gravity, de Sitter, and Swampland Distance Conjectures.

Abstract

We study the charge-to-mass ratios of BPS states in four-dimensional $\mathcal{N}=2$ supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.