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Self-duality, Ramond-Ramond fields and \(K\)-theory. (English) Zbl 0990.81626
Summary: Just as D-brane charge of Type IIA and Type IIB superstrings is classified, respectively, by \(K^1(X)\) and \(K(X)\), Ramond-Ramond fields in these theories are classified, respectively, by \(K(X)\) and \(K^1(X)\). 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.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
19-XX \(K\)-theory
58J99 Partial differential equations on manifolds; differential operators
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