Construction of modular branching functions from Bethe's equations in the 3-state Potts chain

DOI10.1007/BF01049953zbMath0945.82507arXivhep-th/9210129MaRDI QIDQ1279260

Rinat Kedem, Barry M. McCoy

Publication date: 31 May 1999

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9210129

zbMATH Keywords

conformal field theoryaffine Lie algebrasquasiparticlesparafermionsmodular invariant partition function

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (16)

The many faces of a character ⋮ Polynomial fermionic forms for the branching functions of the rational coset conformal field theories \(\widehat{su}(2)_M\times\widehat{su}(2)_N/\widehat{su}(2)_{M+N}\) ⋮ Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries ⋮ 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 ⋮ Fermionic expressions for the characters of \(c_{p,1}\) logarithmic conformal field theories ⋮ Combinatorial constructions of modules for infinite-dimensional Lie algebras. I: Principal subspace ⋮ Integrable anyon chains: from fusion rules to face models to effective field theories ⋮ 3-manifolds and VOA characters ⋮ Nahm sums, quiver a-polynomials and topological recursion ⋮ Spaces of coinvariants and fusion product. I: From equivalence theorem to Kostka polynomials ⋮ Fermionic characters and arbitrary highest-weight integrable \({\widehat{\mathfrak{sl}}}_{r+1}\)-modules ⋮ Z_nclock models and chains ofso(n)₂non-Abelian anyons: symmetries, integrable points and low energy properties ⋮ Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾ ⋮ Fermionic counting of RSOS states and Virasoro character formulas for the unitary minimal series \(M(\nu,\nu+1)\): Exact results ⋮ Anyonic interpretation of Virasoro characters and the thermodynamic Bethe ansatz ⋮ Numerical results for the three-state critical Potts model on finite rectangular lattices.

Cites Work

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• Operator content of two-dimensional conformally invariant theories
• Conformal weights of RSOS lattice models and their fusion hierarchies
• Verma modules over the Virasoro algebra
• Ocneanu cell calculus and integrable lattice models
• Infinite-dimensional Lie algebras, theta functions and modular forms
• Modular and conformal invariance constraints in representation theory of affine algebras
• Modular invariant partition functions in two dimensions
• Analytical calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons
• Level-rank duality in nonunitary coset theories
• G_N ⊗ G_L/G_N+L CONFORMAL FIELD THEORIES AND THEIR MODULAR INVARIANT PARTITION FUNCTIONS
• Structure of the Standard Modules for the Affine Lie Algebra 𝐴⁽¹⁾₁
• A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
• SPECTRUM AND COMPLETENESS OF THE INTEGRABLE 3-STATE POTTS MODEL: A FINITE SIZE STUDY
• ROW TRANSFER MATRIX FUNCTIONAL EQUATIONS FOR A–D–E LATTICE MODELS
• ‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle
• Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

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