Loop formulation of supersymmetric Yang-Mills quantum mechanics

TL;DR

This paper develops a loop formulation for N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice, enabling better control of fermion sign problems and offering an alternative simulation approach.

Contribution

It introduces a fermion loop formulation and a reduced fermion matrix determinant for improved lattice simulations of supersymmetric quantum mechanics.

Findings

Separation of partition function into bosonic and fermionic parts.

Control of fermion sign problems in numerical simulations.

An alternative approach using reduced fermion matrix determinants.

Abstract

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.