Relationship between various supersymmetric lattice models

TL;DR

This paper explores the close relationships among various supersymmetric lattice models, showing how they can be derived from one another through field truncation and highlighting their structural similarities.

Contribution

It clarifies the connections between different supersymmetric lattice models, demonstrating how models by Catterall, Sugino, and CKKU relate through field truncation and reduction.

Findings

Catterall's N=(2,2) model is similar to Sugino's model after removing extra degrees of freedom.

The N=(2,2) models can be derived from the N=(4,4) orbifold lattice theory.

Removing extra degrees of freedom from Catterall's model preserves supersymmetry.

Abstract

We comment on the relationships between several supersymmetric lattice models; the ``orbifold lattice theory'' by Cohen-Kaplan-Katz-Unsal (CKKU), lattice regularization of the topological field theory by Sugino and the ``geometrical approach'' by Catterall. We point out that these three models have close relationships; the N =(2,2) model by Catterall [Catterall] and the two-dimensional N = (2,2) lattice theory being similar to Sugino's construction [Sugino] can be derived by appropriate truncation of fields in the two-dimensional N = (4,4) orbifold lattice theory by CKKU [Cohen et al]. Catterall's N = (2,2) description possesses extra degrees of freedom compared to the target N = (2,2) theory. If we remove those extra degrees of freedom in a way keeping supersymmetry on the lattice, Catterall's description reduces to a model of the Sugino type.