Towards extending the Chern-Simons couplings at order $O(\alpha'^2)$

TL;DR

This paper investigates the consistency of recently proposed Chern-Simons couplings on D-branes at order $O(\alpha'^2)$ by comparing them with S-matrix calculations, confirming their invariance under T-duality and gauge transformations.

Contribution

It extends the understanding of Chern-Simons couplings at higher order by verifying their consistency with S-matrix elements and symmetry transformations.

Findings

S-matrix reproduces proposed couplings and additional terms.

All couplings are invariant under linear T-duality.

Couplings respect B-field gauge invariance.

Abstract

Using the compatibility of the anomalous Chern-Simons couplings on D$_p$-branes with the linear T-duality and with the antisymmetric B-field gauge transformations, some couplings have been recently found for $C^{(p-3)}$ at order $O(\alpha'^2)$. We examine these couplings with the S-matrix element of one RR and two antisymmetric B-field vertex operators. We find that the S-matrix element reproduces these couplings as well as some other couplings. Each of them is invariant under the linear T-duality and the B-field gauge transformations.