Supersymmetry breaking in the three-dimensional nonlinear sigma model

TL;DR

This paper investigates the phase structure of a three-dimensional supersymmetric nonlinear sigma model with explicit supersymmetry breaking, revealing two phases with massive fermions and a metastable vacuum, using effective potential analysis.

Contribution

It introduces a deformed supersymmetric sigma model with explicit supersymmetry breaking and analyzes its phase structure using the tadpole method and 1/N expansion.

Findings

Fundamental fermions become massive in both phases.

The O(N) symmetric phase has a metastable vacuum.

Two distinct phases are identified, similar to the ordinary model.

Abstract

In this work we discuss the phase structure of a deformed supersymmetric nonlinear sigma model in a three-dimensional space-time. The deformation is introduced by a term that breaks supersymmetry explicitly, through imposing a slightly different constraint to the fundamental superfields of the model. Using the tadpole method, we compute the effective potential at leading order in 1/N expansion. From the gap equations, i.e., conditions that minimize the effective potential, we observe that this model presents two phases as the ordinary model, with two remarkable differences: 1) the fundamental fermionic field becomes massive in both phases of the model, which is closely related to the supersymmetry breaking term; 2) the O(N) symmetric phase presents a meta-stable vacuum.