T-duality of curvature terms in D-brane actions

TL;DR

This work addresses the mismatch between T-duality and curvature terms in the D-brane DBI action by constructing linear-order T-duality invariant curvature completions that consistently couple to the NSNS B-field. The author builds explicit T-dual completions for all curvature-squared terms, showing how B-field terms can be organized into the three-form field strength $H=dB$ and matching the $O(α'^2)$ disk amplitude for two NSNS states. The analysis also clarifies the role of the dilaton, arguing that no derivative dilaton terms appear in the string-frame action at this order and deriving Einstein-frame dilaton couplings from graviton-to-dilaton replacements in the string-frame curvature terms. The resulting action provides a T-duality consistent, amplitude-matched correction to the D-brane DBI action, valid for both constant and non-constant dilaton, and highlights how a Gauss-Bonnet-like combination emerges with cancellations of non-tensor pieces.

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(α'^2) terms of the corresponding disk-level scattering amplitude.