The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups

TL;DR

This paper analyzes the vacuum structure of N=2 supersymmetric QCD with classical gauge groups SO(n) and Sp(2n), revealing exact S-dualities, symmetry breaking patterns, and monodromies through hyperelliptic Riemann surfaces.

Contribution

It extends the analysis of vacuum structures to SO(n) and Sp(2n) gauge groups, providing explicit solutions and dualities, building upon prior SU(n) results.

Findings

Solutions expressed via hyperelliptic Riemann surfaces of genus equal to the gauge group's rank.

Exact S-dualities acting on couplings and masses in scale-invariant cases.

Reproduction of symmetry breaking patterns and prediction of weak-coupling monodromies.

Abstract

We determine the vacuum structure of N=2 supersymmetric QCD with fundamental quarks for gauge groups SO(n) and Sp(2n), extending prior results for SU(n). The solutions are all given in terms of families of hyperelliptic Riemann surfaces of genus equal to the rank of the gauge group. In the scale invariant cases, the solutions all have exact S-dualities which act on the couplings by subgroups of PSL(2,Z) and on the masses by outer automorphisms of the flavor symmetry. They are shown to reproduce the complete pattern of symmetry breaking on the Coulomb branch and predict the correct weak--coupling monodromies. Simple breakings with squark vevs provide further consistency checks involving strong--coupling physics.