Renormalization Group Improvement and Dynamical Breaking of Symmetry in a Supersymmetric Chern-Simons-matter Model

TL;DR

This paper explores how the Renormalization Group Equation influences the effective superpotential and symmetry breaking in a supersymmetric Chern-Simons-matter model, revealing limited impact of RGE improvements compared to non-supersymmetric cases.

Contribution

It demonstrates the application of RGE to improve the effective superpotential calculation in a supersymmetric model and compares its effects to non-supersymmetric scenarios.

Findings

RGE can be used to sum leading and next-to-leading logs in the superpotential.

Radiative corrections break classical scale invariance.

RGE improvements have limited effects in supersymmetric models.

Abstract

In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2+1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.