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

Abstract

The one loop correction to the SUSY Ward-Takahashi identity is calculated on the lattice with a Wilson fermion. The supersymmetry on the lattice is broken explicitly by the gluino mass and the lattice artifact. We should fine-tune the parameters in the theory to the point given by the additive mass correction in order to eliminate the breaking effect of the 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 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. The operator mixing of the supercurrent is also investigated. We find that the supercurrent mixes only with a gauge-invariant current Tμ which is related to the gamma-trace anomaly. ©2000 The American Physical Society.