It is well-known that Noether currents in the classical four-dimensional $N=1$ supersymmetric Yang--Mills theory 4D $N=1$ SYM, i.e., the $U1_A$ current, the supersymmetry SUSY current and the energy-momentum tensor, form a multiplet under SUSY, called the Ferrara--Zumino supermultiplet. Inspired by this structure, we define the energy-momentum tensor in the lattice formulation of 4D $N=1$ SYM by a renormalized super transformation of a lattice SUSY current. By using a renormalized SUSY Ward--Takahashi relation, the energy-momentum tensor so constructed is shown to conserve in the quantum continuum limit. Our construction of the energy-momentum tensor is very explicit and usable in non-perturbative numerical simulations.

Ferrara--Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM