Relationship between various supersymmetric lattice models

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 = (2, 2) model by Catterall [1] and the two-dimensional = (2, 2) lattice theory being similar to Sugino's construction [2] can be derived by appropriate truncation of fields in the two-dimensional = (4, 4) orbifold lattice theory by CKKU [3]. Catterall's = (2, 2) description possesses extra degrees of freedom compared to the target = (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.