Numerical investigations of Supersymmetric Yang-Mills Quantum Mechanics with 4 supercharges

TL;DR

This paper presents non-perturbative numerical studies of supersymmetric Yang-Mills quantum mechanics with 4 supercharges, using two methods to explore the spectrum for SU(2) and SU(3) gauge groups.

Contribution

It introduces and applies two independent numerical methods to analyze the spectrum of the model, including the first spectrum calculation for SU(3) with all fermionic sectors.

Findings

Calculated the spectrum for SU(3) in all fermionic sectors.

Reproduced the low-energy spectrum for SU(2) using Monte Carlo methods.

Proposed a method to access observables in different Hilbert space sectors via imaginary chemical potential.

Abstract

We report on our non-perturbative investigations of supersymmetric Yang-Mills quantum mechanics with 4 supercharges. We employ two independent numerical methods. First of them is the cut Fock space method whose numerical implementation was recently generalized to include the SU(N) gauge group. It allowed us to calculate for the first time the spectrum of the model with SU(3) symmetry in all fermionic sectors. Independently, we implemented the Rational Hybrid Monte Carlo algorithm and reproduced the accessible part of the low-energy spectrum of the model with SU(2) gauge symmetry. We argue that by simulating at imaginary chemical potential one can get access to observables defined in sectors of Hilbert space with a given quark number.