The K-Theoretic Formulation of D-Brane Aharonov-Bohm Phases

TL;DR

This paper develops a K-theoretic framework to compute D-brane Aharonov-Bohm phases, providing both topological and analytic methods, and applies it to specific string theory configurations.

Contribution

It introduces a novel K-theoretic approach to calculate D-brane Aharonov-Bohm phases, linking topological pairings with eta-invariants for the first time.

Findings

Derived explicit formulas for torsion flux phases.

Established the existence and well-definedness of K-theoretic pairings.

Validated the approach with a Type I string theory experiment.

Abstract

The topological calculation of Aharonov-Bohm phases associated with D-branes in the absence of a Neveu-Schwarz B-field is explored. The K-theoretic classification of Ramond-Ramond fields in Type II and Type I theories is used to produce formulae for the Aharonov-Bohm phase associated with a torsion flux. A topological construction shows that K-theoretic pairings to calculate such phases exist and are well-defined. An analytic perspective is then taken, obtaining a means for determining Aharonov-Bohm phases by way of the reduced eta-invariant. This perspective is used to calculate the phase for an experiment involving the $(-1)-8$ system in Type I theory, and compared with previous calculations performed using different methods.