Ferrara–Zumino supermultiplet and the energy–momentum tensor in the lattice formulation of 4D N=1N=1 SYM

It is well-known that Noether currents in the classical four-dimensional N=1N=1 supersymmetric Yang–Mills theory (4D N=1N=1 SYM), i.e., the U(1)AU(1)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=1N=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 be conserved in the quantum continuum limit. Our construction of the energy–momentum tensor is very explicit and usable in non-perturbative numerical simulations.