Derivative corrections to D-brane actions with constant background fields

TL;DR

This work computes the complete disk-level derivative corrections to a single D-brane action in type II string theory with constant background fields, delivering the first nontrivial corrections at order $\alpha'^2$ for both the Born-Infeld and Wess-Zumino sectors. By employing a boundary-state, string-sigma-model approach, the authors express the corrections in terms of a tensor built from the gauge field strength, effectively encoding them as the Riemann tensor of a non-symmetric metric $h = \delta + F$, and they derive all $2n$-form, $2n$-derivative WZ corrections alongside four-derivative BI corrections with all orders of $F$. The results are cross-checked against known $t_8$-type structures, reduced consistently to lower dimensions via T-duality, and linked to curvature-based corrections (e.g., second fundamental form and Green–Bachas results). The non-symmetric gravity interpretation provides a unifying geometric picture and hints at deeper connections to dualities and background independence in D-brane effective actions.

Abstract

We study derivative corrections to the effective action for a single D-brane in type II superstring theory coupled to constant background fields. In particular, within this setting we determine the complete expression for the (disk level) four-derivative corrections to the Born-Infeld part of the action. We also determine 2n-form 2n-derivative corrections to the Wess-Zumino term. Both types of corrections involve all orders of the gauge field strength, F. The results are obtained via string sigma-model loop calculations using the boundary state operator language. The corrections can be succinctly written in terms of the Riemann tensor for a non-symmetric metric.