Bound state transformation walls

TL;DR

This paper introduces 'bound state transformation walls' in N=2 supergravity, explaining how bound states change across these walls without changing their index, and explores their implications near singularities with massless particles.

Contribution

It reveals the existence of bound state transformation walls and characterizes phenomena like recombination and conjugation, providing new insights into BPS spectrum behavior.

Findings

Bound state transformation walls resolve paradoxes in moduli space.

Recombination and conjugation are two phenomena occurring on these walls.

Constraints on BPS spectrum near singularities with massless particles are derived.

Abstract

In four dimensional N=2 supergravity theories, BPS bound states near marginal stability are described by configurations of widely separated constituents with nearly parallel central charges. When the vacuum moduli can be dialed adiabatically until the central charges become anti -parallel, a paradox arises. We show that this paradox is always resolved by the existence of "bound state transformation walls" across which the nature of the bound state changes, although the index does not jump. We find that there are two distinct phenomena that can take place on these walls, which we call recombination and conjugation. The latter is associated to the presence of singularities at finite distance in moduli space. Consistency of conjugation and wall-crossing rules near these singularities leads to new constraints on the BPS spectrum. Singular loci supporting massless vector bosons are particularly subtle in this respect. We argue that the spectrum at such loci necessarily contains massless magnetic monopoles, and that bound states around them transform by intricate hybrids of conjugation and recombination.