In this work, we discuss the phase structure of a deformed $\mathcal{N}=1$ 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 a $1/N$ 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 metastable vacuum.

• Received 25 July 2013

DOI:https://doi.org/10.1103/PhysRevD.88.067702