Gradient flow equation in SQCD

TL;DR

This paper introduces a supersymmetric gradient flow equation for ${\cal N}=1$ SQCD in four dimensions, derived in superfield formalism and shown to preserve supersymmetry in a gauge covariant way.

Contribution

It presents the first formulation of a supersymmetric gradient flow in four-dimensional SQCD, ensuring compatibility with supersymmetry and gauge invariance.

Findings

Flow equation derived in superfield formalism.

Flow for component fields is supersymmetric up to gauge transformations.

Flow time derivative commutes with supersymmetry transformations.

Abstract

We propose a supersymmetric gradient flow in ${\cal N}=1$ SQCD in four dimensions. The flow equation is derived in the superfield formalism and is also given for component fields of the Wess-Zumino gauge in a gauge covariant manner. We find that the flow for the component fields is supersymmetric in a sense that the flow time derivative and any supersymmetry transformation commute with each other up to a gauge transformation.