Polynomial Fermionic Forms for the Branching Functions of the Rational Coset Conformal Field Theories $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$}

Abstract

General fermionic expressions for the branching functions of the rational coset conformal field theories $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$ 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 $q\to q^{-1}$.

40 pages, LATEX, no figures; revised version to appear in Nuclear Physics B

References in corpus (13)

• Fermionic Sum Representations for Conformal Field Theory Characters
• Fermionic Quasi-Particle Representations for Characters of $(G^{(1)}{)}_1\times (G^{(1)}{)}_1ø(G^{(1)}{)}_2$
• Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
• Fermionic Character Sums and the Corner Transfer Matrix
• Quasi-Particles, Conformal Field Theory, and $q$-Series
• Construction of Modular Branching Functions from Bethe's Equations in the 3-State Potts Chain
• Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model
• Exceptional structure of the dilute A${}_3$ model: E${}_8$ and E${}_7$ Rogers--Ramanujan identities
• The Many Faces of a Character
• Polynomial identities of the Rogers--Ramanujan type
• Path Spaces and W-Fusion in Minimal Models
• Dilogarithm identities, fusion rules and structure constants of CFTs
• Explicit Construction of $N=2$ $W_3$ Current in the $N=2$ Coset $\frac{SU(3)}{SU(2)\times U(1)}$ Model

Cited by in corpus (16)

• Parafermion Hall states from coset projections of abelian conformal theories
• Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories
• 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
• Bailey flows and Bose-Fermi identities for the conformal coset models $(A_1^{(1)}{)}_N\times (A_1^{(1)}{)}_{N^{\prime }}/(A_1^{(1)}{)}_{N+N^{\prime }}$
• The perturbations ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ of the minimal models $M(p,p^{\prime })$ and the trinomial analogue of Bailey's lemma
• N=2 Supersymmetry and Bailey Pairs
• Exclusion statistics in conformal field theory and the UCPF for WZW models
• $q$-Trinomial identities
• Strings, paths, and standard tableaux
• Coset construction of logarithmic minimal models: branching rules and branching functions
• Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots
• Central Charge and the Andrews-Bailey Construction
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models
• A quartet of fermionic expressions for $M(k,2k\pm 1)$ Virasoro characters via half-lattice paths
• Local height probabilities in a composite Andrews-Baxter-Forrester model