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 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.

26 pages, no figure, (v3) modified the eq. (3.15) and (3.18) and related statement in the derivation of Sugino model from the Catterall model in the previous version (v2)

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