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

TL;DR

This paper develops a method using the gradient flow to construct a renormalized supercurrent in 4D $\\mathcal{N}=1$ super Yang--Mills theory on the lattice, enabling better analysis of supersymmetry in lattice regularizations.

Contribution

It applies the gradient flow method to derive the renormalized supercurrent on the lattice for 4D $\mathcal{N}=1$ SYM, expressing it in terms of flowed fields at one-loop level.

Findings

Derived the lattice supercurrent expression using gradient flow.

Expressed the supercurrent in terms of flowed gauge and gaugino fields.

Performed the calculation at one-loop level in the Wess--Zumino gauge.

Abstract

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].