Self-Duality, Ramond-Ramond Fields, and K-Theory

TL;DR

This paper explores the classification of Ramond-Ramond fields in superstring theories using K-theory, revealing corrections to the Dirac quantization formula due to curvature, brane charges, and fermion anomalies.

Contribution

It provides a detailed analysis of quantum self-duality of RR fields and incorporates K-theory to account for anomaly-related corrections in the quantization formula.

Findings

RR fields classified by K-theory groups K(X) and K^1(X)

Corrections to Dirac quantization include curvature and anomaly effects

Fermion anomalies require K-theory for proper description

Abstract

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.