A note on the center of mass in non-commutative theories

TL;DR

This paper investigates the center of mass in non-commutative gauge theories, specifically for D-branes on a non-commutative torus, clarifying how to decouple the U(1) sector from internal dynamics.

Contribution

It provides a method to identify the decoupled U(1) center of mass sector in non-commutative U(N) gauge theories on a torus, addressing coupling issues.

Findings

Decoupled U(1) sector can be correctly identified in non-commutative theories.

Internal dynamics are described in momentum space, not as SU(N) valued fields.

Coupling between center of mass and internal degrees of freedom is clarified.

Abstract

The dynamics of a stack of N D-branes is described by U(N) gauge theory of which the central U(1) describes the center of mass motion and the remaining SU(N) describes the internal dynamics. In the non-commutative situation, these two parts are coupled by the *-commutator interaction. We describe here how to identify the correct decoupled U(1) center of mass subsector of U(N) gauge theory for the case of the non-commutative torus. The internal dynamics remainder is not a theory of SU(N) valued fields but has a simple description in momentum space.