K-theoretical boundary rings in N=2 coset models

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

2004-08-08

arxiv.org/abs/hep-th/0408060v2

Nucl.Phys. B706 (2005) 531-548

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, harvmac (b); reference added, table 2 beautified

Scientific paper

10.1016/j.nuclphysb.2004.11.037

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.

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