The Strong-Coupling Spectrum of the Seiberg-Witten Theory

TL;DR

This paper analyzes the spectrum of BPS states in N=2 supersymmetric SU(2) Yang-Mills theory, revealing the stable particles in strong coupling and providing a unified view of the spectrum across coupling regimes.

Contribution

It offers a novel analysis of the global structure of the Seiberg-Witten solution, identifying stable BPS states in strong coupling without semi-classical methods.

Findings

Only magnetic monopole and dyon are stable in strong coupling.

The spectrum at weak coupling is recovered without semi-classical approximations.

BPS state disintegration across the coupling boundary is characterized.

Abstract

We carefully study the global structure of the solution of the $N=2$ supersymmetric pure Yang-Mills theory with gauge group $SU(2)$ obtained by Seiberg and Witten. We exploit its ${\bf Z}_2$-symmetry and describe the curve in moduli space where BPS states can become unstable, separating the strong-coupling from the weak-coupling region. This allows us to obtain the spectrum of stable BPS states in the strong-coupling region: we prove that only the two particles responsible for the singularities of the solution (the magnetic monopole and the dyon of unit electric charge) are present in this region. Our method also permits us to very easily obtain the well-known weak-coupling spectrum, without using semi-classical methods. We discuss how the BPS states disintegrate when crossing the border from the weak to the strong-coupling region.