S-matrix elements from T-duality

Abstract

Recently it has been speculated that the S-matrix elements satisfy the Ward identity associated with the T-duality. This indicates that a group of S-matrix elements is invariant under the linear T-duality transformations on the external states. If one evaluates one component of such T-dual multiplet, then all other components may be found by the simple use of the linear T-duality. The assumption that fields must be independent of the Killing coordinate, however, may cause, in some cases, the T-dual multiplet not to be gauge invariant. In those cases, the S-matrix elements contain more than one T-dual multiplet which are intertwined by the gauge symmetry. In this paper, we apply the T-dual Ward identity on the S-matrix element of one RR $(p-3)$-form and two NSNS states on the world volume of a D${}_p$-brane to find its corresponding T-dual multiplet. In the case that the RR potential has two transverse indices, the T-dual multiplet is gauge invariant, however, in the case that it has one transverse index the multiplet is not gauge invariant. We find a new T-dual multiplet in this case by imposing the gauge symmetry. We show that the multiplets are reproduced by explicit calculation, and their low energy contact terms at order ${\alpha }^{\prime 2}$ are consistent with the existing couplings in the literature.

33 pages, Latex file, the version appears in NPB

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Cited by in corpus (16)

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• Ricci curvature corrections to type II supergravity
• On Higher Derivative Couplings in Theories with Sixteen Supersymmetries
• Ramond-Ramond corrections to type II supergravity at order ${\alpha }^{\prime 3}$
• Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism
• Ramond-Ramond S-matrix elements from T-dual Ward identity
• Higher derivative corrections to WZ action: One RR, one NSNS and one NS couplings
• S-duality constraint on higher-derivative couplings
• Three-Point Disc Amplitudes in the RNS Formalism
• T-duality of ${\alpha }^{\prime }$-correction to DBI action at all orders of gauge field
• 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
• BCFW Deformation and Regge Limit
• On Chern-Simons Couplings at order $O({\alpha }^{\prime 2})$
• S-matrix element of two R-R and one NS states