On $(α')^2$ corrections to the D-brane action for non-geodesic world-volume embeddings

TL;DR

This work computes disk-level five-point string amplitudes to determine the complete α'^2 corrections to the D-brane Dirac-Born-Infeld action for curved backgrounds with non-geodesic embeddings. By comparing string amplitudes to an augmented DBI action containing ambiguous curvature terms, the authors relate and constrain the coefficients of these terms. They show that, using a Type IIA–heterotic duality argument, the coefficients c_1, c_2, c_3 can be fixed to zero, while c_4 and c_5 remain undetermined due to field-redefinition freedoms that do not affect on-shell S-matrix elements. Overall, the results validate the BachasCurvature proposal up to terms that vanish on the lowest-order equations of motion, and provide a complete analysis of α'^2 derivative corrections for general ambient geometries and embeddings.

Abstract

In hep-th/9903210 (curvature)$^2$ terms of the effective D-brane action were derived to lowest order in the string coupling. Their results are correct up to ambiguous terms which involve the second fundamental form of the D-brane. We compute five point string amplitudes on the disk. We compare the subleading order in $α'$ of the string amplitudes with the proposed lagrangian of hep-th/9903210 supplemented by the ambiguous terms. The comparison determines the complete form of the gravitational terms in the effective D-brane action to order ${\calO}(α^{' 2})$. Our results are valid for arbitrary ambient geometries and world-volume embeddings.