General covariance of the non-abelian DBI-action: Checks and Balances

TL;DR

This paper tests a proposed method to ensure diffeomorphism invariance in the non-abelian D0-brane DBI action, confirming its consistency with T-duality, curved metrics, and higher-order velocities, and analyzing the symmetrized trace approximation.

Contribution

It introduces and validates a basepoint independence approach for non-abelian DBI actions, extending its applicability to curved metrics and higher velocity orders.

Findings

T-duality correctly interchanges potential and kinetic terms.

Basepoint independence method works for curved metrics with a physical gauge.

Method applies to higher order velocities, clarifying the symmetrized trace approximation.

Abstract

We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a basepoint independence constraint between matrix Riemann normal coordinate systems. First we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose basepoint independence using an auxiliary dN^2-dimensional non-linear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order four, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action.