On Non-Abelian Structure From Matrix Coordinates

TL;DR

This paper explores how matrix coordinates of D0-branes in a RR background induce non-Abelian gauge symmetries, revealing a connection between D0-brane dynamics and non-Abelian gauge theories.

Contribution

It demonstrates that matrix coordinate transformations lead to non-Abelian gauge-like symmetries in D0-brane systems, linking string theory and gauge theory concepts.

Findings

Matrix coordinate transformations induce non-Abelian gauge symmetries.

Derived Lorentz-like equations of motion for matrix coordinates.

Field strengths transform in the adjoint representation of U(N).

Abstract

We consider the matrix quantum mechanics of N D0-branes in the background of the 1-form RR field. It is observed that the transformations of matrix coordinates of D0-branes induce on the Abelian RR field symmetry transformations that are like those of non-Abelian gauge fields. The Lorentz-like equations of motion for matrix coordinates are derived. The field strengths appearing in the Lorentz-like equations transform in the adjoint representation of U(N) under symmetry transformations. A possible relation between D0-brane dynamics in RR background, and the semi-classical dynamics of charged particles in Yang-Mills background is mentioned.