Lattice Actions for Yang-Mills Quantum Mechanics with Exact Supersymmetry

TL;DR

This paper develops lattice actions for supersymmetric Yang-Mills quantum mechanics with exact supersymmetry at finite lattice spacing, derived from twisted higher-dimensional theories, enabling non-perturbative studies of supersymmetric models.

Contribution

It introduces new lattice formulations for supersymmetric quantum mechanics with exact supersymmetry, obtained via dimensional reduction from twisted super Yang-Mills theories in higher dimensions.

Findings

Lattice actions preserve exact supersymmetry at non-zero lattice spacing.

Derived models include $ ext{Q}=4,8,16$ supercharges.

Framework facilitates non-perturbative investigations of supersymmetric theories.

Abstract

We derive lattice actions for Yang-Mills quantum mechanics for models with $\cQ=4, 8$ and 16 supercharges which possess an exact supersymmetry at non-zero lattice spacing. These are obtained by dimensional reduction of twisted versions of the corresponding super Yang-Mills theories in $D=2, 3$ and 4 dimensions.