One loop calculation of SUSY Ward-Takahashi identity on lattice with Wilson fermion

TL;DR

This paper calculates the one-loop correction to the SUSY Ward-Takahashi identity on the lattice with Wilson fermions, showing how to fine-tune parameters to restore supersymmetry and analyzing operator mixing effects.

Contribution

It demonstrates the equivalence of additive mass corrections from SUSY Ward-Takahashi identity and axial symmetry, enabling simultaneous restoration of symmetries with a single fine tuning.

Findings

Additive mass correction from SUSY identity matches axial symmetry correction.

Supercurrent mixes only with a gauge invariant current related to gamma-trace anomaly.

Both key symmetries can be restored in the continuum with one fine tuning.

Abstract

One loop correction to the SUSY Ward-Takahashi identity is calculated on lattice with Wilson fermion. The supersymmetry on lattice is broken explicitly by the gluino mass and the lattice artifact. We should fine tune parameters in the theory to the point given by the additive mass correction in order to eliminate the breaking effect of lattice artifact. It is shown that the additive mass correction appearing from the SUSY Ward-Takahashi identity coincide with that from the axial $U(1)_R$ symmetry as was suggested by Curci and Veneziano. Two important symmetries of the super Yang-Mills theory can be recovered simultaneously in the continuum with a single fine tuning. Operator mixing of the supercurrent are also investigated. We find that the supercurrent mixes only with a gauge invariant current $T_\mu$ which is related to the gamma-trace anomaly.