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

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• T-duality of anomalous Chern-Simons couplings
• T-duality of the Riemann curvature corrections to supergravity
• Ricci curvature corrections to type II supergravity
• Four-Derivative Brane Couplings from String Amplitudes
• S-matrix elements from T-duality
• On Higher Derivative Couplings in Theories with Sixteen Supersymmetries
• Disc amplitudes, picture changing and space-time actions
• Ramond-Ramond corrections to type II supergravity at order ${\alpha }^{\prime 3}$
• Ramond-Ramond S-matrix elements from T-dual Ward identity
• New Examples of Flux Vacua
• Tree-level S-matrix elements from S-duality
• Higher derivative corrections to WZ action: One RR, one NSNS and one NS couplings
• An off-shell D-brane action at order ${\alpha }^{\prime 2}$ in flat spacetime
• S-duality of color-ordered amplitudes
• S-duality constraint on higher-derivative couplings
• Brane Curvature Corrections to the $\mathcal{N}=1$ Type II/F-theory Effective Action
• T-dual RR couplings on D-branes from S-matrix elements
• On Chern-Simons Couplings at order $O({\alpha }^{\prime 2})$