4D $\mathcal{N}=1$ SYM supercurrent on the lattice in terms of the gradient flow

The gradient flow[1-5] gives rise to a versatile method to construct renormalized composite operators in a regularization-independent manner. By adopting this method, the authors of~Refs.[6-9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D $\mathcal{N}=1$ super Yang--Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess--Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields[10].