Soft Supersymmetry Breaking in Deformed Moduli Spaces, Conformal Theories, and N = 2 Yang-Mills Theory

TL;DR

This paper explores non-perturbative effects of small soft supersymmetry breaking in various supersymmetric theories, providing new derivations and analyzing the impact on vacuum structure and phases, including in N=2 Yang-Mills theory.

Contribution

It offers a new anomaly-based derivation of soft breaking effects and thoroughly analyzes their influence on moduli spaces, vacua, and phases in supersymmetric gauge theories.

Findings

Complete determination of vacuum expectation values in SU(2) with deformed moduli space.

Relation between modulus and prepotential derived using superfield spurion analysis.

Soft scalar masses can induce a transition to a free Coulomb phase.

Abstract

We give a self-contained discussion of recent progress in computing the non-perturbative effects of small non-holomorphic soft supersymmetry breaking, including a simple new derivation of these results based on an anomaly-free gauged U(1)_R background. We apply these results to N = 1 theories with deformed moduli spaces and conformal fixed points. In an SU(2) theory with a deformed moduli space, we completely determine the vacuum expectation values and induced soft masses. We then consider the most general soft breaking of supersymmetry in N = 2 SU(2) super-Yang-Mills theory. An N = 2 superfield spurion analysis is used to give an elementary derivation of the relation between the modulus and the prepotential in the effective theory. This analysis also allows us to determine the non-perturbative effects of all soft terms except a non-holomorphic scalar mass, away from the monopole points. We then use an N = 1 spurion analysis to determine the effects of the most general soft breaking, and also analyze the monopole points. We show that naive dimensional analysis works perfectly. Also, a soft mass for the scalar in this theory forces the theory into a free Coulomb phase.