Supersymmetric gradient flow in N=1 SYM

The gradient flow equation is derived in N=1 supersymmetric Yang-Mills theory in terms of the component field of the Wess-Zumino gauge. We show that the flow-time derivative and supersymmetry transformation that is naively extended to five dimensions commute with each other up to a gauge transformation. In this sense, the obtained flow is supersymmetric in the Wess-Zumino gauge. We also discuss more about the symmetry of the flow equation.Comment: 24 page

Supersymmetric gradient flow in 4d N=1 SQCD

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.Comment: 5 page