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 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.

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

References in corpus (6)

• Twisted K-theory and loop group representations
• K-Theory from a physical perspective
• Abelian and non-Abelian branes in WZW models and gerbes
• Gerbes, (twisted) K-theory, and the supersymmetric WZW model
• Boundary RG Flows of N=2 Minimal Models
• D-branes in N=2 coset models and twisted equivariant K-theory

Cited by in corpus (6)

• Fusion of symmetric $D$-branes and Verlinde rings
• D-Brane Charges in Gepner Models
• D-branes and matrix factorisations in supersymmetric coset models
• Modular Invariants and Twisted Equivariant K-theory
• Kondo flow invariants, twisted K-theory and Ramond-Ramond charges
• Kernel solutions of the Kostant operator on eight-dimensional quotient spaces