Anomalous couplings for D-branes and O-planes
Jose F. Morales, Claudio A. Scrucca, Marco Serone
TL;DR
By performing one-loop RR-channel factorization on annulus, Möbius strip, and Klein bottle amplitudes, Morales, Scrucca, and Serone derive the complete anomalous Wess-Zumino couplings for D-branes and Op-planes in general backgrounds. They show that gravitational couplings for D-branes are governed by the A-roof genus $\\hat{\\mathcal A}$ and those for Op-planes by the Hirzebruch polynomial $\\hat{\\mathcal L}$, with precise tangent- and normal-bundle curvature dependence. Normal-bundle couplings arise from ratios of these polynomials between tangent and normal sectors, and are corroborated by a sigma-model derivation that confirms the results across general $p$. Consistency with Type I anomaly cancellation fixes key normalization factors and supports an anomaly-inflow interpretation, underscoring the topological and exact nature of these couplings with potential implications for string compactifications.
Abstract
We study anomalous Wess-Zumino couplings of D-branes and O-planes in a general background and derive them from a direct string computation by factorizing in the RR channel various one-loop amplitudes. In particular, we find that Op-planes present gravitational anomalous couplings involving the Hirzebruch polynomial L, similarly to the roof genus A encoding Dp-brane anomalous couplings. We determine, in each case, the precise dependence of these couplings on the curvature of the tangent and normal bundles.