Supersymmetric gradient flow in $$\mathcal{N}=1$$ SYM

Abstract The gradient flow equation is derived in four-dimensional $$\mathcal{N}=1$$ 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 4+1 dimensions by replacing the four-dimensional fields with the corresponding flowed fields 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.