On Ramond-Ramond fields and K-theory

TL;DR

This paper explores the relationship between Ramond-Ramond fields in superstring theory and K-theory, demonstrating how their coupling to D-branes cancels anomalies, thus providing a deeper mathematical understanding of string theory phenomena.

Contribution

It extends previous work by expressing Ramond-Ramond field couplings in K-theory and showing anomaly cancellation in both Type IIA and IIB string theories.

Findings

Coupling of Ramond-Ramond fields to D-branes is expressed in K-theoretic terms.

Anomaly cancellation between Ramond-Ramond coupling and fermions on D-branes.

Generalization of previous results to broader contexts in string theory.

Abstract

A recent paper by Moore and Witten explained that Ramond-Ramond fields in Type II superstring theory have a global meaning in K-theory. In this note we amplify and generalize some points raised in that paper. In particular, we express the coupling of the Ramond-Ramond fields to D-branes in a K-theoretic framework and show that the anomaly in this coupling exactly cancels the anomaly from the fermions on the brane, both in Type IIA and Type IIB.