Discontinuous BPS spectra in $N = 2$ gauge theory

TL;DR

This paper studies the discontinuous changes in BPS spectra in four-dimensional N=2 gauge theories, revealing how the number of soliton states varies across marginal stability boundaries, with implications for understanding non-perturbative phenomena.

Contribution

It provides a semiclassical analysis of BPS spectrum discontinuities in N=2 gauge theories, specifically quantifying how soliton state counts change across stability walls.

Findings

Number of soliton states changes by a factor of 2^{Q·Q'} across stability walls.

Decay of quark-soliton bound states analyzed in weak coupling limit.

Spectrum discontinuities depend on the symplectic product of charge vectors.

Abstract

We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which can be treated with semiclassical methods in the weak coupling limit, is the decay of quark-soliton bound states. For a quark and a soliton of electric-magnetic charge vectors $Q$ and $Q^\prime$ respectively, we find that as the manifold of marginal stability is crossed, the number of soliton states changes by a factor of $2^{Q \cdot Q^\prime}$, where the dot denotes the symplectic product.