Stability of BPS states and weak coupling limits

We study the stability and spectrum of BPS states in 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 << 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 -> 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.

Automated summary

The study reveals a certain classification of BPS stability that is partially independent of the value of gauge couplings, and mathematically formulates this stability in terms of a limiting mixed Hodge structure associated with the vanishing coupling limit. The implications of the results for the Swampland program, aiming to understand weak-coupling limits, are also examined, particularly regarding the nature and presence of an infinite tower of light charged BPS states.