A Critique of the Link Approach to Exact Lattice Supersymmetry

TL;DR

This paper critically analyzes the link approach for discretizing N=2 super Yang Mills theory on a lattice, revealing fundamental inconsistencies and limitations in preserving supersymmetry.

Contribution

It demonstrates that the link approach cannot preserve all supersymmetries at finite lattice spacing, challenging previous assumptions about lattice supersymmetry constructions.

Findings

The link approach is inconsistent for lattice supersymmetry.

Only one supersymmetry can be preserved on the lattice.

The approach cannot fully discretize the continuum theory while maintaining all supersymmetries.

Abstract

We examine the link approach to constructing a lattice theory of N=2 super Yang Mills theory in two dimensions. The goal of this construction is to provide a discretization of the continuum theory which preserves all supersymmetries at non-zero lattice spacing. We show that this approach suffers from an inconsistency and argue that a maximum of just one of the supersymmetries can be implemented on the lattice.