Remark on the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM

TL;DR

This paper proposes an improved definition of the energy-momentum tensor in lattice 4D $ abla=1$ SYM that better aligns with supersymmetry and reduces renormalization constants needed.

Contribution

It introduces a new formulation of the energy-momentum tensor in lattice supersymmetric Yang--Mills theory that is more consistent with supersymmetry and simplifies renormalization.

Findings

Energy-momentum tensor is conserved in the continuum limit.

Origin of energy aligns with supersymmetry in the new formulation.

Number of renormalization constants reduced from four to two.

Abstract

In a recent paper, arXiv:1209.2473 \cite{Suzuki:2012gi}, we presented a possible definition of the energy-momentum tensor in the lattice formulation of the four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory, that is conserved in the quantum continuum limit. In the present Letter, we propose a quite similar but somewhat different definition of the energy-momentum tensor (that is also conserved in the continuum limit) which is superior in several aspects: In the continuum limit, the origin of the energy automatically becomes consistent with the supersymmetry and the number of renormalization constants that require a (non-perturbative) determination is reduced to two from four, the number of renormalization constants appearing in the construction in Ref. \cite{Suzuki:2012gi}.