Lattice models and $N=2$ supersymmetry

TL;DR

This paper reviews the construction of exactly solvable lattice models that correspond to continuum $N=2$ supersymmetric theories, focusing on topological sectors and their physical implications.

Contribution

It introduces a method to construct lattice models with topological sectors that match $N=2$ supersymmetric field theories, including both critical and off-critical cases.

Findings

Identification of lattice models with topological sectors

Recovery of $N=2$ supersymmetric theories from lattice models

Discussion of scattering matrices for excitations

Abstract

We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural topological sectors, and then identify the continuum limits of these sectors with topologically twisted $N=2$ supersymmetric field theories. From this, we then describe how to recover the complete lattice versions of the $N=2$ supersymmetric field theories. We discuss a number of simple physical examples and we describe how to construct a broad class of models. We also give a brief review of the scattering matrices for the excitations of these models. (Contribution to the procedings of the Cargese meeting on ``String Theory, Conformal Models and Topological Field Theories'', May 12-21, 1993.)