Test for the Myers-Chern-Simons Action

TL;DR

This paper extends the gauge transformation framework for nonabelian fields on branes and verifies the gauge invariance of the Myers Chern-Simons action up to fifth order, confirming its consistency with RR field interactions.

Contribution

It generalizes the infinitesimal gauge transformation for nonabelian brane fields and tests the Myers Chern-Simons action's gauge invariance at higher orders.

Findings

Gauge invariance holds up to fifth order in  for D-instantons.

Supports the validity of the Myers formula for brane interactions.

Provides a higher-order consistency check for nonabelian gauge theories on branes.

Abstract

We present a generalization of the infinitesimal gauge transformation for nonabelian fields on the stack of branes up to the third order in $\Phi$. We test the gauge invariance of the action up to the fifth order in $\Phi$ for $D$-instantons. This substantiates the Myers formula for the Chern-Simons term in action, which describes interaction with the RR fields of $N$ coincident $\Dp$ branes.