Lattice Sigma Models with Exact Supersymmetry

TL;DR

This paper constructs lattice sigma models with exact fermionic symmetry that preserve supersymmetry in the continuum limit, using twisted formulations and numerical simulations.

Contribution

It introduces discretized, twisted lattice sigma models with exact supersymmetry and demonstrates their invariance under additional symmetries, reducing fine-tuning needs.

Findings

Models exhibit exact fermionic symmetry on the lattice.

Additional discrete symmetries are present in 2D and 4D models.

Preliminary numerical results support theoretical predictions.

Abstract

We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and {\it twisted} versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and in many cases admit a Wilson term to suppress doubles. In the two and four dimensional theorie s we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions.