T-duality of anomalous Chern-Simons couplings

TL;DR

This work addresses the incompatibility of the anomalous D-brane Chern-Simons couplings with T-duality by performing a linear T-duality guided reconstruction of higher-derivative couplings. The author builds a complete $O(\alpha'^2)$ T-dual multiplet for the RR potentials ${\cal C}^{(p-3)}$, ${\cal C}^{(p-1)}$, ${\cal C}^{(p+1)}$, and ${\cal C}^{(p+3)}$, combining multiple T-dual pieces to obtain covariant and $B$-field gauge-invariant expressions (up to contact-term and massless-pole subtleties). S-matrix considerations are used to fix ambiguities and to ensure consistency with duality and gauge symmetries, including the appearance of Mandelstam-variable dependent terms that must be matched with poles. The results provide explicit covariant forms for the higher-derivative CS couplings on D-branes under T-duality, aligning field-theory completions with string-theory scattering amplitudes and clarifying the role of the S-matrix as the duality-invariant object.

Abstract

It is known that the anomalous D$_p$-brane Chern-Simons couplings are not consistent with the standard rules of T-duality. Using compatibility of these couplings with the linear T-duality transformations, the B-field gauge transformations and with the general coordinate transformations as guiding principles we find new couplings at order $O(α'^2)$ for ${\cal C}^{(p-3)}$, ${\cal C}^{(p-1)}$, ${\cal C}^{(p+1)}$ and ${\cal C}^{(p+3)}$.