BPS Geodesics in N=2 Supersymmetric Yang-Mills Theory

TL;DR

This paper develops new techniques to analyze geodesics on Seiberg-Witten surfaces, which correspond to BPS states in N=2 supersymmetric Yang-Mills theory, enabling a better understanding of the BPS spectrum across different phases.

Contribution

It introduces methods for global analysis of geodesics on Seiberg-Witten surfaces, facilitating the study of BPS spectra in various N=2 Yang-Mills theories.

Findings

Recovered known results for pure SU(2) gauge theory

Extended analysis to SU(2) with massive adjoint matter

Demonstrated effectiveness of new methods in different phases

Abstract

We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric $ds^2 = |\lambda_{SW}|^2$. Because the existence of such geodesics implies the existence of BPS states in N=2 supersymmetric Yang-Mills theory, one can use these methods to study the BPS spectrum in various phases of the Yang-Mills theory. By way of illustration, we show how, using our new methods, one can easily recover the known results for the N=2 supersymmetric SU(2) pure gauge theory, and we show in detail how it also works for the N=2, SU(2) theory coupled to a massive adjoint matter multiplet.