S-matrix elements from T-duality

TL;DR

This paper investigates how S-matrix elements on D-branes transform under T-duality, revealing gauge invariance issues and constructing T-dual multiplets that match low-energy couplings.

Contribution

It applies T-dual Ward identities to specific S-matrix elements, identifying gauge-invariant multiplets and constructing new ones when gauge invariance is broken.

Findings

T-dual multiplets can be gauge invariant or intertwined by gauge symmetry.

Explicit calculations confirm the T-dual multiplets and their low-energy limits.

The results are consistent with known couplings in the literature.

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 $\alpha'^2$ are consistent with the existing couplings in the literature.