Gravitational Couplings of D-branes and O-planes
B. Stefanski
TL;DR
The work addresses how D-branes and orientifold planes acquire gravitational Wess-Zumino couplings by explicit worldsheet scattering of gravitons and RR potentials on D-brane and O-plane boundaries. Using boundary-state and crosscap formalisms, it computes four- and eight-form amplitudes and shows the results match the predicted D-brane actions involving the A-roof genus and the orientifold actions involving the Hirzebruch L polynomial, including the correct relative factors. The calculations also verify Green-Schwarz gravitational anomaly cancellation in Type I via the O9-plane contributions, providing nontrivial evidence for the consistency of orientifold constructions. Overall, the paper strengthens the link between string amplitudes and the topological WZ couplings that govern D-brane and O-plane dynamics and anomaly inflow.
Abstract
An explicit calculation is performed to check all the tangent bundle gravitational couplings of Dirichlet branes and Orientifold planes by scattering $q$ gravitons with a $p+1$ form Ramond-Ramond potential in the world-volume of a $D(p+2q)$-brane. The structure of the D-brane Wess-Zumino term in the world-volume action is confirmed, while a different O-plane Wess-Zumino action is obtained.