Massive super Yang-Mills quantum mechanics: classification and the relation to supermembrane

TL;DR

This paper classifies all supersymmetric mass deformations of super Yang-Mills quantum mechanics derived from various spacetime dimensions, linking them to supermembrane descriptions in supergravity backgrounds and generalizing p-brane formulations.

Contribution

It provides a comprehensive classification of supersymmetric mass deformations across multiple dimensions and relates these to supermembrane matrix models and generalized p-brane actions.

Findings

Classified supersymmetric mass deformations for super Yang-Mills quantum mechanics.

Connected matrix models to supermembrane descriptions in supergravity backgrounds.

Extended light-cone p-brane formulations to include time-dependent backgrounds.

Abstract

We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.