Exact Lattice Supersymmetry at the Quantum Level for N=2 Wess-Zumino models in Lower Dimensions

TL;DR

This paper demonstrates that a recently proposed non-local lattice formulation of N=2 Wess-Zumino models maintains exact supersymmetry at the quantum level, confirmed through Ward-Takahashi identities up to two loops.

Contribution

It provides evidence that exact lattice supersymmetry can be preserved at the quantum level in lower-dimensional models using a non-local formulation.

Findings

Supersymmetry remains exact at two-loop quantum corrections.

Ward-Takahashi identities are satisfied in the proposed lattice model.

The non-local star product preserves the Leibniz rule on the lattice.

Abstract

We have recently proposed a new lattice SUSY formulation which has exact lattice supersymmetry for Wess-Zumino models in one and two dimensions for all N=2 supercharges. This formulation is non-local in the coordinate space but the difference operator satisfies the Leibniz rule on the newly defined star product. Here we show that this lattice supersymmetry is kept exact at the quantum level by investigating Ward-Takahashi identities up to two loop level.