Simple Models in Supersymmetric Quantum Mechanics on a Graph

TL;DR

This paper explores supersymmetric quantum mechanics models constructed on graphs, introducing discrete versions of Gaussian and Wess-Zumino models, and proposing supersymmetric extensions of Lee-Wick and Galileon models with multiple supersymmetries.

Contribution

It presents novel graph-based discretizations of supersymmetric models and introduces new supersymmetric extensions of known theories, including models with multiple supersymmetries.

Findings

Discrete Gaussian and Wess-Zumino models on graphs analyzed.

Topological index as a multiple integral discussed.

Supersymmetric extensions of Lee-Wick and Galileon models proposed.

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.