Extended Supersymmetric Moduli Space and a SUSY/Non-SUSY Duality

TL;DR

This paper explores the full moduli space of N=1 supersymmetric U(N) gauge theories with a superpotential, revealing a novel supersymmetry breaking mechanism linked to negative squared gauge couplings and proposing a new duality involving field-dependent couplings.

Contribution

It introduces a comprehensive analysis of the moduli space including higher-dimensional operators and establishes a new duality between supersymmetric and softly broken gauge theories.

Findings

Supersymmetry can be spontaneously broken when the gauge coupling squared becomes negative.

The full IR superpotential can be computed using diagrammatic, matrix model, and string theoretic methods.

A new duality relates theories with field-dependent gauge couplings to those with spurion-induced supersymmetry breaking.

Abstract

We study N=1 supersymmetric U(N) gauge theories coupled to an adjoint chiral field with superpotential. We consider the full supersymmetric moduli space of these theories obtained by adding all allowed chiral operators. These include higher-dimensional operators that introduce a field-dependence for the gauge coupling. We show how Feynman diagram/matrix model/string theoretic techniques can all be used to compute the IR glueball superpotential. Moreover, in the limit of turning off the superpotential, this leads to a deformation of N=2 Seiberg-Witten theory. In the case where the superpotential drives the squared gauge coupling to a negative value, we find that supersymmetry is spontaneously broken, which can be viewed as a novel mechanism for breaking supersymmetry. We propose a new duality between a class of N=1 supersymmetric U(N) gauge theories with field-dependent gauge couplings and a class of U(N) gauge theories where supersymmetry is softly broken by nonzero expectation values for auxiliary components of spurion superfields.