On RR couplings on D-branes at order $O({\alpha }^{\prime 2})$

Abstract

Recently, it has been found that there are couplings of the RR field strength $F^{(p)}$ and the B-field strength $H$ on the world volume of D${}_p$-branes at order $\mathcal{O}({\alpha }^{\prime 2})$. These couplings which have both world-volume and transverse indices, are invariant under the linear T-duality transformations. Consistency with the nonlinear T-duality indicates that the RR field strength $F^{(p)}$ in these couplings should be replaced by ${\mathcal{F}}^{(p)}=d{\mathcal{C}}^{(p-1)}$ where $\mathcal{C}=e^{B}C$. This replacement, however, reproduces some non-gauge invariant terms. On the other hand, the nonlinear terms are invariant under the linear T-duality transformations at the level of two B-fields. This allows one to remove some of the nonlinear terms in ${\mathcal{F}}^{(p)}$. We fix this by comparing the nonlinear couplings with the S-matrix element of one RR and two NSNS vertex operators. Our results indicate that in the expansion of ${\mathcal{F}}^{(p)}$ one should keep only the B-field gauge invariant terms, e.g. $B\wedge d{C}^{(p-3)}$ where both indices of B-field lie along the brane. Moreover, in this case one should replace $B$ with $B+2\pi {\alpha }^{\prime }f$ to have the $B$-field gauge invariance.

23 pages, Latex file, 1 figure; v2:typos corrected, to appear in JHEP

References in corpus (6)

• More on WZ action of non-BPS branes
• Higher Derivative Brane Couplings from T-Duality
• Ramond-Ramond field strength couplings on D-branes
• T-duality of anomalous Chern-Simons couplings
• Higher Loop Spin Field Correlators in Various Dimensions
• Disk level S-matrix elements at eikonal Regge limit

Cited by in corpus (1)

• T-duality of anomalous Chern-Simons couplings