A supersymmetric matrix model: III. Hidden SUSY in statistical systems

TL;DR

This paper reveals hidden supersymmetry in statistical systems derived from a supersymmetric matrix model, connecting ground states of certain XXZ chains to supersymmetric vacua and uncovering new spectral relations.

Contribution

It demonstrates that blocks of a supersymmetric matrix model can be mapped to non-supersymmetric statistical systems, revealing hidden supersymmetry and linking to Razumov--Stroganov conjectures.

Findings

Most blocks map to non-supersymmetric 1+1D systems

Ground states of XXZ chains with specific parameters are supersymmetric vacua

Spectral relations suggest hidden supersymmetry in statistical models

Abstract

The Hamiltonian of a recently proposed supersymmetric matrix model has been shown to become block-diagonal in the large-N, infinite 't Hooft coupling limit. We show that (most of) these blocks can be mapped into seemingly non-supersymmetric $(1+1)$-dimensional statistical systems, thus implying non-trivial (and apparently yet-unknown) relations within their spectra. Furthermore, the ground states of XXZ-chains with an odd number of sites and asymmetry parameter $\Delta = - 1/2$, objects of the much-discussed Razumov--Stroganov conjectures, turn out to be just the strong-coupling supersymmetric vacua of our matrix model.