Supersymmetry Breaking in Graph Quantum Mechanics

TL;DR

This paper introduces a graph-based model for supersymmetric quantum mechanics, showing that supersymmetry is preserved on finite graphs and analyzing its behavior under graph modifications.

Contribution

It develops a discrete graph theoretic framework for supersymmetric quantum mechanics and proves key properties including the impossibility of spontaneous supersymmetry breaking on finite graphs.

Findings

Supersymmetry can be naturally modeled on finite graphs.

Supersymmetry cannot be spontaneously broken in the graph model.

Edge rewiring affects supersymmetric properties in predictable ways.

Abstract

In this paper, we develop the groundwork for a graph theoretic toy model of supersymmetric quantum mechanics. Using discrete Witten-Morse theory, we demonstrate that finite graphs have a natural supersymmetric structure and use this structure to incorporate supersymmetry into an existing model of graph quantum mechanics. We prove that although key characteristics of continuum supersymmetric systems are preserved on finite unweighted graphs, supersymmetry cannot be spontaneously broken. Finally, we prove new results about the behavior of supersymmetric graph quantum systems under edge rewiring.