Comparing two definitions for gauge variations of dielectric D-branes

TL;DR

This paper compares two gauge variation definitions for dielectric D-branes, establishing their equivalence for R-R variations but not for NS-NS variations, confirming the naive variation as valid.

Contribution

It demonstrates the equivalence of two gauge variation definitions for R-R fields and clarifies the validity of the naive variation for NS-NS fields in non-Abelian D-brane actions.

Findings

R-R variations are invariant under both definitions.

Naive NS-NS variation is the only valid definition.

The action's invariance under R-R variations is proven.

Abstract

We compare two definitions of gauge variations in the case of non-Abelian actions for multiple D-branes. Equivalence is proven for the R-R variations, which shows that the action is invariant also under the easier, naive variation. For the NS-NS variations however, the two definitions are not equivalent, leaving the naive definition as the only valid one.