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

TL;DR

The paper extends Chern-Simons couplings on D_p-branes to order O(α'^2) by enforcing compatibility with linear T-duality and B-field gauge invariance, and tests these structures against a disk-level S-matrix for one RR state and two B-fields. By computing the string amplitude and performing a low-energy expansion, the authors extract both massless open-string poles and contact terms, which are then reproduced in field theory using the DBI/CS action plus new B-field–invariant couplings; the RR gauge symmetry is preserved in the sum of all contributions. The results validate the proposed C^{(p-3)} couplings and reveal additional T-duality–invariant, gauge-invariant B-field couplings, with the open-string pole structure fixed by normalization and the contact terms matching the effective Lagrangian. The work underscores the consistency of higher-derivative CS couplings with linear T-duality and RR gauge symmetry and points to further work extending these analyses to other RR forms to complete T-duality multiplets.

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 $O(α'^2)$. 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.