Spontaneous breaking of superconformal invariance in (2+1)D supersymmetric Chern-Simons-matter theories in the large N limit

TL;DR

This paper investigates how superconformal and gauge symmetries can spontaneously break in three-dimensional supersymmetric Chern-Simons-matter theories at large N, highlighting the role of the Coleman-Weinberg mechanism in N=1 models.

Contribution

It computes the effective superpotential at subleading order and demonstrates the dynamical mass generation via the Coleman-Weinberg mechanism in N=1 models, contrasting with N=2 models.

Findings

Coleman-Weinberg mechanism induces mass scale in N=1 models

Two-loop diagrams are responsible for symmetry breaking

Mechanism fails in N=2 supersymmetric models

Abstract

In this work it is studied the spontaneous breaking of superconformal and gauge invariances in the Abelian N=1,2 three-dimensional supersymmetric Chern-Simons-matter theories in a large N limit. It is computed the K\"ahlerian effective superpotential at subleading order and shown that the Coleman-Weinberg mechanism is the responsible for the dynamical generation of a mass scale in the N=1 model. This effect appears due to two-loop diagrams that are logarithmic divergent. In particular, the Coleman-Weinberg mechanism fails when we lift the N=1 to N=2 Supersymmetric Chern-Simons-Matter model, like what happens in a perturbative expansion in the coupling constants.