Renormalization group improvement and dynamical breaking of symmetry in a supersymmetric Chern–Simons-matter model

A.G Quinto,A.F Ferrari,A.C Lehum

doi:10.1016/j.nuclphysb.2016.04.015

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.

Highlights

Dynamical Symmetry Breaking (DSB) constitutes a very appealing scenario in field theory, where quantum corrections are entirely responsible for the appearance of nontrivial minima of the effective potential [1]
The effective superpotential K (σ) is well suited for the approach we develop in this work, since we will be able to calculate it by using a simple ansatz, using the information already known from the literature regarding renormalization group functions for the model (3)
The mechanism of symmetry breaking is central for the formulation of a consistent quantum field theory of the known elementary interactions, and the possibility that quantum corrections of a symmetric potential could alone induce such symmetry breaking is a rather interesting one, for its mathematical elegance, and for physical reasons

Summary

INTRODUCTION

Dynamical Symmetry Breaking (DSB) constitutes a very appealing scenario in field theory, where quantum corrections are entirely responsible for the appearance of nontrivial minima of the effective potential [1]. Relaxing the requirement of manifest N = 8 supersymmetry, this approach can be generalized to a N = 6 Chern-Simons-matter theory with the gauge group Uk(N ) × U−k(N ) (k and −k are CS levels) [35, 36], which is expected to be enhanced to N = 8 for k = 1 or k = 2 [37,38,39] The quantization of such model was thoroughly studied in [40,41,42,43,44,45,46,47,48]. The first part of our work is the computation of the effective superpotential of a generic supersymmetric CS theory coupled to matter superfields, up to two-loops To this end, we use the RGE and the β and γ function calculated in [17, 51], avoiding the direct computation of any supergraph. Some explicit results and the Mathematica code used to obtain them is given as a Supplementary Material to this work

CALCULATION OF THE EFFECTIVE SUPERPOTENTIAL

RGE IMPROVEMENT IN THE THREE DIMENSIONAL SUPERSYMMETRIC CASE

DYNAMICAL BREAKING OF SYMMETRY

CONCLUSIONS