Supersymmetric gradient flow in 4d N=1 SQCD

TL;DR

This paper introduces a supersymmetric gradient flow for 4d N=1 SQCD, defining flow equations in superfield and component forms, and explores a simplified flow using SYM action gradients.

Contribution

It proposes a novel supersymmetric gradient flow for 4d N=1 SQCD, including superfield and component formulations, and discusses a simplified flow based on SYM action.

Findings

Flow equations are supersymmetric up to gauge transformations.

Component flow equations are gauge covariant and supersymmetric.

A simplified flow using SYM action gradient is discussed.

Abstract

A supersymmetric gradient flow for four-dimensional N=1 supersymmetric QCD (SQCD) is proposed. The flow equation is given in both the superfield and component fields of the Wess-Zumino gauge. The superfield flow equation is defined for each of the gauge and matter multiplets individually. Adding a gauge fixing, the component-field flow equation is defined in the Wess-Zumino gauge in a gauge covariant manner. We find that the latter equation is supersymmetric in a sense that the commutator of the flow time derivative and the supersymmetry transformation vanishes up to a gauge transformation. We also discuss a simplified flow by using the gradient of supersymmetric Yang-Mills (SYM) action instead of using SQCD action to define a gauge multiplet flow.