Path Spaces and W-Fusion in Minimal Models

Abstract

Product forms of characters of Virasoro minimal models are obtained which factorize into $(2,\odd)\times(3,\even)$ characters. These are related by generalized Rogers-Ramanujan identities to sum forms allowing for a quasiparticle interpretation. The corresponding dilogarithm identities are given and the factorization is used to analyse the related path space structure as well as the fusion of the maximally extended chiral algebra.

11 pages, TeX, minor adjustment to journal version, 4 PostScript figures in tar-archive (appendix, to be printed manually)

References in corpus (4)

• Dilogarithm Identities in Conformal Field Theory
• Lift of dilogarithm to partition identities
• Fusion Algebras of Fermionic Rational Conformal Field Theories via a Generalized Verlinde Formula
• Virasoro Representations on Fusion Graphs

Cited by in corpus (13)

• Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
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• Virasoro character identities from the Andrews--Bailey construction
• Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4ν)
• Multinomials and Polynomial Bosonic Forms for the Branching Functions of the $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$ Conformal Coset Models
• Modular Invariance and Uniqueness of Conformal Characters
• Product Expansions of Conformal Characters
• Polynomial Fermionic Forms for the Branching Functions of the Rational Coset Conformal Field Theories $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$}
• Ising model conformal boundary conditions from open string field theory
• Closed form fermionic expressions for the Macdonald index
• Fusion Algebras and Characters of Rational Conformal Field Theories
• Steps towards Lattice Virasoro Algebras: su(1,1)
• From path representations to global morphisms for a class of minimal models