K-theoretical boundary rings in N=2 coset models

TL;DR

This paper explores the connection between twisted equivariant K-theory and boundary rings in N=2 coset conformal field theories, revealing structural similarities and differences with chiral rings and providing explicit formulas for Verlinde algebra ranks.

Contribution

It introduces a K-theoretical boundary ring for N=2 coset models and computes the associated twisted equivariant K-theories for hermitian symmetric spaces.

Findings

K-theory boundary rings have the same rank as N=2 chiral rings

The product structure in K-theory differs from that of chiral primaries

Explicit formulas for Verlinde algebra ranks are provided

Abstract

A boundary ring for N=2 coset conformal field theories is defined in terms of a twisted equivariant K-theory. The twisted equivariant K-theories K_H(G) for compact Lie groups (G, H) such that G/H is hermitian symmetric are computed. These turn out to have the same ranks as the N=2 chiral rings of the associated coset conformal field theories, however the product structure differs from that on chiral primaries. In view of the K-theory classification of D-brane charges this suggests an interpretation of the twisted K-theory as a `boundary ring'. Complementing this, the N=2 chiral ring is studied in view of the isomorphism between the Verlinde algebra V_k(G) and twisted K_G(G) as proven by Freed, Hopkins and Teleman. As a spin-off, we provide explicit formulae for the ranks of the Verlinde algebras.