Anomalous D-brane and orientifold couplings from the boundary state

TL;DR

Problem: verify anomalous couplings in D-brane and orientifold actions by direct string amplitudes. Approach: boundary-state computations of RR and NS-NS scattering in the presence of a D-brane or crosscap, extracting $B\wedge {\cal C}_{p-1}$ and ${\rm tr\,}R^2\wedge {\cal C}_{p-3}$ couplings and comparing to the Wess-Zumino action. Key findings: the D9-brane and O9-plane couple to the first Pontrjagin class $p_1(\hat{R})$ with the expected relative strength; for orientifolds the crosscap calculation reproduces the Das result up to the $32$ normalization, yielding a half-strength relative to D-branes. Significance: strengthens the consistency of anomaly-related couplings in string theory and demonstrates the boundary-state method as a robust tool for deriving higher-curvature interactions.

Abstract

We compute scattering amplitudes involving both R-R and NS-NS fields in the presence of a D-brane or orientifold plane. These provide direct evidence for the anomalous couplings in the D-brane and orientifold actions. The D9-brane and O9-plane are found to couple to the first Pontrjagin class with the expected relative strength.