Supersymmetric matrix models and branched polymers

TL;DR

This paper solves a supersymmetric matrix model with a general potential, revealing that supersymmetry causes only branched polymer diagrams to remain, leading to a novel eigenvalue distribution near the critical point.

Contribution

It introduces a solution to a supersymmetric matrix model that highlights the dominance of branched polymers due to supersymmetry, with a new eigenvalue distribution at criticality.

Findings

Supersymmetry cancels bosonic and fermionic loops, leaving branched polymers.

Eigenvalue distribution near critical point is of a new kind.

Matrix models typically describe surfaces, but here they relate to branched polymers.

Abstract

We solve a supersymmetric matrix model with a general potential. While matrix models usually describe surfaces, supersymmetry enforces a cancellation of bosonic and fermionic loops and only diagrams corresponding to so-called branched polymers survive. The eigenvalue distribution of the random matrices near the critical point is of a new kind.