Duality in N=2 SUSY Gauge Theories: low-energy effective action and BPS spectra

TL;DR

This paper reviews the low-energy effective action and BPS spectra in N=2 supersymmetric SU(2) gauge theories, emphasizing duality, supersymmetry constraints, and the impact of matter hypermultiplets, including non-trivial conformal field theories.

Contribution

It provides a detailed analysis of how duality and supersymmetry constraints determine the BPS spectra in N=2 SU(2) gauge theories, including cases with matter hypermultiplets and Argyres-Douglas points.

Findings

Determination of BPS spectra across moduli space using duality and symmetries.

Identification of non-trivial conformal points with matter hypermultiplets.

Insights into the structure of low-energy effective actions in N=2 theories.

Abstract

After an introduction to N=2 susy Yang-Mills theories, I review in some detail, for the SU(2) gauge group, how the low-energy effective action is obtained using duality and the constraints arising from the supersymmetry. Then I discuss how knowledge of this action, duality and certain discrete symmetries allow us to determine the spectra of stable BPS states at any point in moduli space. This is done for gauge group SU(2), without and with fundamental matter hypermultiplets which may have non-vanishing bare masses. In the latter case non-trivial four-dimensional CFTs arise at Argyres-Douglas type points.