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

## TL;DR

This paper develops a method to represent the supercurrent in 4D N=1 super Yang--Mills theory using the gradient flow, aiding lattice simulations and supersymmetry restoration.

## Contribution

It applies the gradient flow technique to construct a properly normalized supercurrent in 4D N=1 SYM, facilitating numerical studies and supersymmetry checks.

## Key findings

- Provides a representation of the supercurrent suitable for lattice simulations
- Enables the use of supercurrent conservation as a criterion for supersymmetry restoration
- Offers a regularization-independent method for supercurrent analysis

## Abstract

The gradient flow and its small flow-time expansion provide a very versatile method to represent renormalized composite operators in a regularization-independent manner. This technique has been utilized to construct typical Noether currents such as the energy--momentum tensor and the axial-vector current in lattice gauge theory. In this paper, we apply the same technique to the supercurrent in the four-dimensional $\mathcal{N}=1$ super Yang--Mills theory (4D $\mathcal{N}=1$ SYM) in the Wess--Zumino gauge. Since this approach provides a priori a representation of the properly normalized conserved supercurrent, our result should be useful, e.g., in lattice numerical simulations of the 4D $\mathcal{N}=1$ SYM; the conservation of the so-constructed supercurrent can be used as a criterion for the supersymmetric point toward which the gluino mass is tuned.