K-theoretical boundary rings in $N=2$ coset models

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 τ ( 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 K G τ ( G ) as proven by Freed, Hopkins and Teleman. As a spin-off, we provide explicit formulae for the ranks of the Verlinde algebras