T-duality of anomalous Chern-Simons couplings

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 $O({\alpha }^{\mathrm{\prime }2})$ for ${\cal C}^{(p-3)}$,${\cal C}^{(p-1)}$,${\cal C}^{(p+1)}$and${\cal C}^{(p+3)}$.