T-duality of curvature terms in D-brane actions

TL;DR

This paper investigates how curvature terms in D-brane actions transform under T-duality, ensuring consistency with scattering amplitudes and including NS-NS B-field contributions.

Contribution

It introduces the correct NS-NS B-field terms into the D-brane action to maintain T-duality invariance at the curvature level, aligning with scattering amplitude results.

Findings

Curvature terms are consistent with T-duality when B-field terms are included.

The modified action reproduces known scattering amplitudes at O(α'^2).

T-duality constrains the form of curvature and B-field terms in D-brane actions.

Abstract

We examine the known curvature terms in the DBI part of the D-brane action under the T-duality transformation. Using the compatibility of the action with the standard rules of T-duality at the linear order as a guiding principle, we include the appropriate NS-NS $B$-field terms in the action and show that they reproduce the O(\alpha'^2) terms of the corresponding disk-level scattering amplitude.