Simple Models in Supersymmetric Quantum Mechanics on a Graph

Abstract

We study some sorts of dimensionally-deconstructed models for supersymmetric (Euclidean) quantum mechanics, or zero-dimensional field theory. In these models, we assign bosonic and fermionic variables to vertices and edges of a graph. We investigate a discrete version for the Gaussian model and the Wess-Zumino-type model on a graph. The topological index as a multiple integral is discussed on these models. In addition, we propose simple examples for supersymmetric extensions of the Lee-Wick model and the Galileon model. A model with two supersymmetries is also provided and generalization to `local' supersymmtric models is examined.