Stability of BPS States and Weak Coupling Limits

TL;DR

This paper investigates the stability and spectrum of BPS states in ${ m N}=2$ supergravity, revealing a coupling-independent filtration that constrains BPS decay processes and has implications for the Swampland conjectures.

Contribution

It proves a stability filtration for BPS states in ${ m N}=2$ supergravity, linking it to monodromy weight filtration and weak coupling limits.

Findings

BPS stability exhibits a partial independence from gauge couplings.

A mathematical formulation of stability via monodromy weight filtration.

Implications for the Swampland program and light charged BPS states.

Abstract

We study the stability and spectrum of BPS states in ${\cal N}=2$ supergravity. We find evidence, and prove for a large class of cases, that BPS stability exhibits a certain filtration which is partially independent of the value of the gauge couplings. Specifically, for any perturbative value of any gauge coupling $g \ll 1$, a BPS state can only decay to some constituents if those constituents do not become infinitely heavier than it in the vanishing coupling limit $g \rightarrow 0$. This stability filtration can be mathematically formulated in terms of the monodromy weight filtration of the limiting mixed Hodge structure associated to the vanishing coupling limit. We study various implications of the result for the Swampland program which aims to understand such weak-coupling limits, specifically regarding the nature and presence of an infinite tower of light charged BPS states.