Phases of N=1 Supersymmetric SO/Sp Gauge Theories via Matrix Model

TL;DR

This paper extends the analysis of N=1 supersymmetric SO/Sp gauge theories using matrix models, deriving complex curves, anomaly equations, and exploring dualities and multiplication maps across different gauge groups.

Contribution

It introduces a comprehensive matrix model approach to analyze N=1 SO/Sp gauge theories, including new multiplication maps and duality insights.

Findings

Derived matrix model complex curves for various superpotential degrees.

Established generalized Konishi anomaly equations with orientifold contributions.

Constructed multiplication maps and identified dualities between different gauge theories.

Abstract

We extend the results of Cachazo, Seiberg and Witten to N=1 supersymmetric gauge theories with gauge groups SO(2N), SO(2N+1) and Sp(2N). By taking the superpotential which is an arbitrary polynomial of adjoint matter \Phi as a small perturbation of N=2 gauge theories, we examine the singular points preserving N=1 supersymmetry in the moduli space where mutually local monopoles become massless. We derive the matrix model complex curve for the whole range of the degree of perturbed superpotential. Then we determine a generalized Konishi anomaly equation implying the orientifold contribution. We turn to the multiplication map and the confinement index K and describe both Coulomb branch and confining branch. In particular, we construct a multiplication map from SO(2N+1) to SO(2KN-K+2) where K is an even integer as well as a multiplication map from SO(2N) to SO(2KN-2K+2) (K is a positive integer), a map from SO(2N+1) to SO(2KN-K+2) (K is an odd integer) and a map from Sp(2N) to Sp(2KN+2K-2). Finally we analyze some examples which show some duality: the same moduli space has two different semiclassical limits corresponding to distinct gauge groups.