Gradient flows in three dimensions

TL;DR

This paper constructs a candidate a-function for three-dimensional Chern-Simons theories with scalars and fermions, showing its monotonic behavior along renormalization group flows in both supersymmetric and non-supersymmetric cases.

Contribution

It introduces a new candidate a-function for 3D Chern-Simons theories, extending the concept of a-function to these models and demonstrating its properties.

Findings

Existence of a candidate a-function in 3D Chern-Simons theories

Monotonic behavior of the a-function along RG flows

Applicability to both supersymmetric and non-supersymmetric cases

Abstract

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We demonstrate the existence of a candidate a-function for renormalisable Chern-Simons theories in three dimensions, involving scalar and fermion fields, in both non-supersymmetric and supersymmetric cases.