The Supersymmetric Ward-Takahashi Identity in 1-Loop Lattice Perturbation Theory. I. General Procedure

Abstract

The one-loop corrections to the lattice supersymmetric Ward-Takahashi identity (WTi) are investigated in the off-shell regime. In the Wilson formulation of the N=1 supersymmetric Yang-Mills (SYM) theory, supersymmetry (SUSY) is broken by the lattice, by the Wilson term and is softly broken by the presence of the gluino mass. However, the renormalization of the supercurrent can be realized in a scheme that restores the continuum supersymmetric WTi (once the on-shell condition is imposed). The general procedure used to calculate the renormalization constants and mixing coefficients for the local supercurrent is presented. The supercurrent not only mixes with the gauge invariant operator $T_{\mu }$. An extra mixing with other operators coming from the WTi appears. This extra mixing survives in the continuum limit in the off-shell regime and cancels out when the on-shell condition is imposed and the renormalized gluino mass is set to zero. Comparison with numerical results are also presented.

16 pages, 2 figures. Typos error corrected

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• Matrix formulation of superspace on 1D lattice with two supercharges
• Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions
• Perturbative renormalization of the supercurrent operator in lattice $\mathcal{N}=1$ supersymmetric Yang-Mills theory