On singular effective superpotentials in supersymmetric gauge theories

TL;DR

This paper investigates singular effective superpotentials in N=1 supersymmetric SU(2) gauge theories with many massless quarks, demonstrating their consistency in describing vacua, RG flow, and higher-derivative terms.

Contribution

It shows that singular superpotentials can accurately describe the moduli space and reproduce known higher-derivative F-terms in supersymmetric gauge theories.

Findings

Superpotentials are singular but consistent with the moduli space.

They correctly reproduce higher-derivative F-terms.

The phenomenon occurs in various dimensions.

Abstract

We study N=1 supersymmetric SU(2) gauge theory in four dimensions with a large number of massless quarks. We argue that effective superpotentials as a function of local gauge-invariant chiral fields should exist for these theories. We show that although the superpotentials are singular, they nevertheless correctly describe the moduli space of vacua, are consistent under RG flow to fewer flavors upon turning on masses, and also reproduce by a tree-level calculation the higher-derivative F-terms calculated by Beasely and Witten (hep-th/0409149) using instanton methods. We note that this phenomenon can also occur in supersymmetric gauge theories in various dimensions.