Curvature terms in D-brane actions and their M-theory origin

TL;DR

This paper derives the complete curvature squared terms in D-brane actions, including non-perturbative corrections, and connects them to M-theory origins, ensuring consistency with dualities and anomaly cancellations.

Contribution

It provides the first derivation of all $(curvature)^2$ terms in D-brane actions at lowest order, including non-perturbative D-instanton effects and M-theory insights.

Findings

Derived $(curvature)^2$ terms matching string amplitudes

Included D-instanton corrections for D3-branes with trivial normal bundle

Connected non-perturbative effects to M5-brane quantum calculations

Abstract

We derive the complete $(curvature)^2$ terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the $o(\alpha'^2)$ corrections to string scattering amplitudes, and are consistent with duality conjectures. In the particular case of the D3-brane with trivial normal bundle, considerations of $SL(2,\mathbb{Z})$ invariance lead to a complete sum of D-instanton corrections for both the parity-conserving and the parity-violating parts of the effective action. These corrections are required for the cancellation of the modular anomalies of massless modes, and are consistent with the absence of chiral anomalies in the intersection domain of pairs of D-branes. We also show that the parity-conserving part of the non-perturbative R^2 action follows from a one-loop quantum calculation in the six-dimensional world-volume of the M5-brane compactified on a two-torus.