zbMATH — the first resource for mathematics

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
Full Text: