Supersymmetric gradient flow in 4d $${{\mathcal {N}}}=1$$ SQCD

Abstract

A supersymmetric gradient flow for four-dimensional \({{\mathcal {N}}}=1\) 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 using the gradient of supersymmetric Yang–Mills (SYM) action instead of using SQCD action to define a gauge multiplet flow.