Supersymmetric N=2 gauge theory with arbitrary gauge group

TL;DR

This paper introduces a universal model for N=2 supersymmetric gauge theories with any gauge group, capturing low-energy dynamics through hyperelliptic curves and matching known limits and dualities.

Contribution

It proposes a new hyperelliptic curve-based model that applies to arbitrary gauge groups, reproduces key physical limits, and aligns with recent dyon charge predictions.

Findings

Reproduces weak and strong coupling limits.

Aligns with recent dyon charge predictions.

Simplifies monopole and dyon spectra when scalar and dual fields align.

Abstract

A new universal model to implement the Seiberg-Witten approach to low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the hyperelliptic curve, whose genus equals the rank of the gauge group. The weak and strong coupling limits are reproduced. The magnetic and electric charges of light dyons, which are present in the proposed model comply with recent predictions derived from the general properties of the theory. The discrete chiral symmetry is implemented, the duality condition is reproduced, and connections between monodromies at weak and strong coupling are established. It is found that the spectra of monopoles and dyons are greatly simplified when vectors representing the scalar and dual fields in the Cartan algebra are aligned along the Weyl vector. This general feature of the theory is used for an additional verification of the model. The model predicts the identical analytic structures of the coupling constants for the theories based on the SU(r+1) and Sp(2r) gauge groups.