Kondo flow invariants, twisted K-theory and Ramond-Ramond charges

TL;DR

This paper explores the relationship between Ramond-Ramond charges, boundary RG flow invariants, and twisted K-theory in super Wess-Zumino-Witten models, establishing a correspondence through algebraic and geometric methods.

Contribution

It introduces a method to associate Kondo RG flow invariants to boundary states and confirms their isomorphism with twisted K-theory, also disproving previous conjectures.

Findings

Invariants match twisted K-theory of the Lie group.

Constructed supersymmetric boundary states and computed their charges.

Disproved two existing conjectures on D-brane charges.

Abstract

We take a worldsheet point of view on the relation between Ramond-Ramond charges, invariants of boundary renormalization group flows and K-theory. In compact super Wess-Zumino-Witten models, we show how to associate invariants of the generalized Kondo renormalization group flows to a given supersymmetric boundary state. The procedure involved is reminiscent of the way one can probe the Ramond-Ramond charge carried by a D-brane in conformal field theory, and the set of these invariants is isomorphic to the twisted K-theory of the Lie group. We construct various supersymmetric boundary states, and we compute the charges of the corresponding D-branes, disproving two conjectures on this subject. We find a complete agreement between our algebraic charges and the geometry of the D-branes.