The a-function for N=2 supersymmetric gauge theories in three dimensions

TL;DR

This paper constructs a more precise a-function for N=2 supersymmetric Chern-Simons theories in three dimensions, involving four-loop calculations to extend previous leading and next-to-leading order results.

Contribution

It develops the next-to-leading order a-function for N=2 supersymmetric Chern-Simons theories, advancing the understanding of renormalization group flows in these models.

Findings

Derived the four-loop renormalization-group functions

Extended the a-function to next-to-leading order for supersymmetric theories

Enhanced the theoretical framework for 3D supersymmetric gauge theories

Abstract

Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.