Test for the Myers–Chern–Simons action

We present a generalization of the infinitesimal gauge transformation for nonabelian fields on the stack of branes up to the third order in Φ. We test the gauge invariance of the action up to the fifth order in Φ 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.