The Coulomb branch of N=1 supersymmetric gauge theory with adjoint and fundamental matter

TL;DR

This paper analyzes the Coulomb branch of N=1 supersymmetric SU(N_c) gauge theories with adjoint and fundamental matter, deriving exact effective couplings and identifying potential superconformal fixed points.

Contribution

It generalizes known N=2 results to N=1 theories by providing exact effective gauge couplings via hyperelliptic curves and exploring the structure of Coulomb branch singularities.

Findings

Exact effective gauge coupling expressed through hyperelliptic curves.

Identification of singular points with potential superconformal fixed points.

Analysis of the Coulomb branch structure for specific N_c and N_f values.

Abstract

We consider N=1 SU(N_c) gauge theory with an adjoint matter field $\Phi$, N_f flavors of fundamentals Q and antifundamentals \tQ, and tree-level superpotential of the form $\tQ\Phi^l Q$. This superpotential is relevant or marginal for $lN_f\leq 2N_c$. The theory has a Coulomb branch which is not lifted by quantum corrections. We find the exact effective gauge coupling on the Coulomb branch in terms of a family of hyperelliptic curves, thus providing a generalization of known results about N=2 SUSY QCD to N=1 context. The Coulomb branch has singular points at which mutually nonlocal dyons become massless. These singularities presumably correspond to new N=1 superconformal fixed points. We discuss them in some detail for N_c=2, N_f=1.