Polynomial fermionic forms for the branching functions of the rational coset conformal field theories

1995/08/31 by Anne Schilling · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions #hep-th

paper · pdf · doi:10.1016/0550-3213(95)00572-2

published as Nucl.Phys. B459 (1996) 393-436 · 40 pages, LATEX, no figures; revised version to appear in Nuclear Physics B

arxiv created 1995/10/31 · openalex publication_date 1996/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

General fermionic expressions for the branching functions of the rational coset conformal field theories \widehatsu(2)_M× \widehatsu(2)_N/\widehatsu(2)_M+N are given. The equality of the bosonic and fermionic representations for the branching functions is proven by introducing polynomial truncations of these branching functions which are the configuration sums of the RSOS models in regime III. The path space interpretation of the RSOS models provides recursion relations for the configuration sums. The proof of the recursion relations for the fermionic expressions is given by using telescopic expansion techniques. The configuration sums of the RSOS model in regime II which correspond to the branching functions of the Z_M+N-parafermion conformal field theory are obtained by the duality transformation q→ q^-1.

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