A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice

TL;DR

This paper introduces a geometrical lattice discretization of two-dimensional N=2 super Yang-Mills theory that maintains gauge invariance and part of the supersymmetry, avoiding spectrum doubling and ensuring a unique vacuum.

Contribution

It presents a novel discretization method based on twisted supersymmetry and Kahler-Dirac fields, preserving key symmetries and avoiding spectrum doubling in lattice super Yang-Mills.

Findings

Lattice action is local with a unique vacuum state.

Spectrum doubling is avoided using Kahler-Dirac fermions.

The approach preserves gauge invariance and part of supersymmetry exactly.

Abstract

We propose a discretization of two dimensional Euclidean Yang-Mills theories with N=2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kahler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once the theory is written in this geometrical language it is straightforward to discretize by mapping the component tensor fields to appropriate geometrical structures in the lattice and by replacing the continuum exterior derivative and its adjoint by appropriate lattice covariant difference operators. The lattice action is local and possesses a unique vacuum state while the use of Kahler-Dirac fermions ensures the model does not exhibit spectrum doubling.