Superspace formulation of the local RG equation

TL;DR

This paper develops a superspace formulation of the local RG equation to analyze supersymmetric RG flows, making holomorphy and R-symmetry constraints explicit, and explores implications for conformal manifolds and the a-function.

Contribution

It introduces a superspace framework for the local RG equation, deriving new consistency conditions and off-criticality expressions for the a-function and a-maximization.

Findings

Derived an expression for the a-function in superspace.

Presented an off-criticality version of the a-maximization equation.

Proved the metric on conformal manifolds is Kahler.

Abstract

We present the superspace formulation of the local RG equation, a framework for the study of supersymmetric RG flows in which the constraints of holomorphy and R-symmetry are manifest. We derive the consistency conditions associated with super-Weyl symmetry off-criticality and initiate the study of their implications. As examples, we derive an expression for the a-function, and present an analog of the a-maximization equation, which is valid off-criticality. We also apply this machinery to the study of conformal manifolds and give a simple proof that the metric on such manifolds is Kahler.