Self-duality, Ramond-Ramond fields and K-theory

Just as D-brane charge of type-IIA and type-IIB superstrings is classified, respectively, by K¹ (X) and K(X), Ramond-Ramond fields in these theories are classified, respectively, by K(X) and K¹ (X). By analyzing a recent proposal for how to interpret quantum self-duality of RR fields, we show that the Dirac quantization formula for the RR p-forms, when properly formulated, receives corrections that reflect curvature, lower brane charges, and an anomaly of D-brane world-volume fermions. The K-theory framework is important here, because the term involving the fermion anomaly cannot be naturally expressed in terms of cohomology and differential forms.