Exact Lattice Supersymmetry from Topological Field Theory

TL;DR

This paper demonstrates how topological field theory techniques can be used to construct lattice supersymmetric theories that preserve exact supersymmetry and maintain Ward identities independent of the cutoff.

Contribution

It introduces a method to derive lattice supersymmetric theories from continuum topological theories, ensuring exact supersymmetry and Ward identity preservation.

Findings

Lattice theories with exact supersymmetry can be constructed from topological field theories.

Ward identities remain valid independently of the lattice cutoff.

The approach leverages metric independence of topological theories to ensure consistency.

Abstract

We discuss the connection between supersymmetric field theories and topological field theories and show how this connection may be used to construct local lattice field theories which maintain an exact supersymmetry. It is shown how metric independence of the continuum topological field theory allows us to derive the lattice theory by blocking out of the continuum in a deformed geometry. This, in turn, allows us to prove the cut-off independence of certain supersymmetric Ward identities.