Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges

TL;DR

This paper develops a Euclidean lattice formulation of a two-dimensional supersymmetric Yang-Mills theory with four supercharges, maintaining one exact supersymmetry to facilitate the correct continuum limit without fine-tuning.

Contribution

It introduces a lattice construction that preserves one supersymmetry exactly, enabling the emergence of the target supersymmetric theory in the continuum limit without fine-tuning.

Findings

Lattice action respects one exact supersymmetry.

Continuum limit reproduces (2,2) supersymmetric Yang-Mills theory.

Method can be generalized to more complex supersymmetric theories.

Abstract

We formulate a Euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions.