K-theoretical boundary rings in N=2 coset models
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 KH(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 Vk(G) and twisted KG(G) as proven by Freed, Hopkins and Teleman. As a spin-off, we provide explicit formulae for the ranks of the Verlinde algebras.
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