K-theoretical boundary rings in image coset models Original Research Article

A boundary ring for image coset conformal field theories is defined in terms of a twisted equivariant K-theory. The twisted equivariant K-theories image for compact Lie groups image such that image is hermitian symmetric are computed. These turn out to have the same ranks as the image 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 image chiral ring is studied in view of the isomorphism between the Verlinde algebra image and image as proven by Freed, Hopkins and Teleman. As a spin-off, we provide explicit formulae for the ranks of the Verlinde algebras.