Supersymmetric Yang-Mills quantum mechanics in various dimensions

TL;DR

This paper discusses supersymmetric Yang-Mills quantum mechanics derived from higher-dimensional theories, exploring its theoretical significance, historical context, and presenting new results for a specific D=4 SU(2) case.

Contribution

It provides new findings for the D=4 SU(2) supersymmetric Yang-Mills quantum mechanics system, expanding understanding of these models.

Findings

New results for D=4 SU(2) SYMQM system

Insights into the relation with M-theory and D0 branes

Historical overview of SYMQM development

Abstract

Supersymmetric Yang-Mills quantum mechanics (SYMQM) results from the dimensional reduction of the Yang-Mills field theory in $D$ space-time dimensions to a single point in the $D-1$ dimensional space. It can be also viewed as the effective quantum mechanics of zero momentum modes of the original theory. These systems were first considered in 80's as simple models with supersymmetry. Independently, zero-volume field theories (especially pure Yang-Mills) were employed as the starting point of the small volume expansion, which is an important theoretical tool complementary to early lattice calculations. Later the models attracted a new wave of interest after the hypothesis of the equivalence, between the $D=10, SU(\infty)$ SYMQM and a M-theory of D0 branes. In this talk some new results obtained for the D=4 system with SU(2) gauge symmetry will be presented.