On the Gauge Invariance of the Chern-Simons Action for N D-Branes

TL;DR

This paper proves the gauge invariance of the Chern-Simons action for N D-branes under RR field transformations and reformulates the action to explicitly show this symmetry.

Contribution

It provides a rigorous proof of gauge invariance and presents a reformulation of the Chern-Simons action to make the symmetry explicit.

Findings

Chern-Simons action is gauge invariant under RR field transformations

Reformulation makes gauge symmetry manifest

Ensures consistency of D-brane effective actions

Abstract

In this short note we provide a proof that the Chern-Simons part of the action for N D-branes is invariant under gauge transformations of the RR fields of the type C_p ->C_p + d\Lambda_{p-1}, and rewrite the action in a form that makes this symmetry manifest.