(Non-)Anomalous D-brane and O-plane couplings: the normal bundle

TL;DR

This work directly computes D-brane and O-plane gravitational couplings including the normal bundle curvature, fixing the normalization unambiguously. By extending two- and four-graviton amplitudes to general momenta and polarizations, it confirms the known anomalous couplings and uncovers non-anomalous eight-form gravitational terms. The results reinforce the consistency of string-derived D-brane/O-plane Wess-Zumino actions and establish a complete, direct check of the normal-bundle contributions, applicable to both D-branes and orientifolds. Overall, the paper clarifies the full gravitational sector of the brane actions and provides a robust string-theory derivation of these couplings.

Abstract

The direct string computation of anomalous D-brane and orientifold plane couplings is extended to include the curvature of the normal bundle. The normalization of these terms is fixed unambiguously. New, non-anomalous gravitational couplings are found.