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

Just as D-brane charge of type-IIA and type-IIB superstrings is clas- sied, respectively, by K 1 (X)and K( X), Ramond-Ramondelds in these theories are classied, respectively, by K(X)and K 1 ( X). Byanalyzing a recent proposal for how to interpret quantum self-duality of RRelds, we show that the Dirac quanti- zation formula for the RR p-forms, when properly formulated, receives corrections thatreflectcurvature,lowerbranecharges,andananomalyofD-braneworld-volume fermions. TheK-theoryframeworkisimportanthere,becausetheterminvolvingthe fermion anomaly cannot be naturally expressed in terms of cohomology and dier- ential forms.