On B-independence of RR charges

TL;DR

This work generalizes the Taylor-Polchinski mechanism for $B$-induced nonlocality of RR charges to a framework with independent odd RR fields and even bulk $B$, showing that after integrating out higher RR fields the effective D-brane couplings to constant RR backgrounds depend only on the world-volume flux $F$, yielding $B$-independent RR charges. By diagonalizing the bulk action with $G = (d + H)C = e^{-B} d e^{B} C$ and applying a de Rham homotopy operator $K$, the authors obtain a local, flux-based expression for charges in the constant RR field limit, namely a coupling of the form $\sum_p \int_{W_{2p+1}} e^{F} C$. The analysis highlights gauge-noninvariance artefacts of the source terms, leading to constraints on brane configurations, and discusses ambiguities that arise when $H$ is cohomologically nontrivial, as illustrated by a 1D toy model with pre-history dependence. These results clarify how RR charges can remain well-defined and quantized despite background $B$-flux in nontrivial topologies, and they illuminate potential physical implications of background flux in brane dynamics.

Abstract

Generalization of the recent Taylor-Polchinski argument is presented, which helps to explain quantization of RR charges in IIA-like theories in the presence of cohomologically trivial H-fields.