Self-Dual Strings and Stability of BPS States in N=2 SU(2) Gauge Theories

TL;DR

This paper demonstrates how BPS states in N=2 SU(2) gauge theories can be understood as self-dual strings on a Riemann surface, providing insights into their stability and behavior at strong coupling.

Contribution

It establishes a novel geometric framework linking BPS states to self-dual strings on Riemann surfaces derived from Calabi-Yau compactifications.

Findings

Proves stability of BPS states using geometric methods

Shows strong coupling behavior of these states

Connects gauge theory states to string theory via Riemann surfaces

Abstract

We show how BPS states of supersymmetric SU(2) Yang-Mills with matter -both massless and massive- are described as self-dual strings on a Riemann surface. This connection enables us to prove the stability and the strong coupling behaviour of these states. The Riemann surface naturally arises from type-IIB Calabi-Yau compactifications whose three-branes wrapped around vanishing two-cycles correspond to one-cycles on this surface.