Anyonic Interpretation of Virasoro Characters and the Thermodynamic Bethe Ansatz

Employing factorized versions of characters as products of quantum dilogarithms corresponding to irreducible representations of the Virasoro algebra, we obtain character formulae which admit an anyonic quasi-particle interpretation in the context of minimal models in conformal field theories. We propose anyonic thermodynamic Bethe ansatz equations, together with their corresponding equation for the Virasoro central charge, on the base of an analysis of the classical limit for the characters and the requirement that the scattering matrices are asymptotically phaseless.Comment: 20 pages (Latex), minor typos corrections and three references adde

Factorized Combinations of Virasoro Characters

We investigate linear combinations of characters for minimal Virasoro models which are representable as a products of several basic blocks. Our analysis is based on consideration of asymptotic behaviour of the characters in the quasi-classical limit. In particular, we introduce a notion of the secondary effective central charge. We find all possible cases for which factorization occurs on the base of the Gauss-Jacobi or the Watson identities. Exploiting these results, we establish various types of identities between different characters. In particular, we present several identities generalizing the Rogers-Ramanujan identities. Applications to quasi-particle representations, modular invariant partition functions, super-conformal theories and conformal models with boundaries are briefly discussed.Comment: 25 pages (LaTex), minor corrections, one reference adde

R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R))

A certain class of unitary representations of U_q(sl(2,R)) has the property of being simultanenously a representation of U_{tilde{q}}(sl(2,R)) for a particular choice of tilde{q}(q). Faddeev has proposed to unify the quantum groups U_q(sl(2,R)) and U_{tilde{q}}(sl(2,R)) into some enlarged object for which he has coined the name ``modular double''. We study the R-operator, the co-product and the Haar-measure for the modular double of U_q(sl(2,R)) and establish their main properties. In particular it is shown that the Clebsch-Gordan maps constructed in [PT2] diagonalize this R-operator.Comment: 27 pages, LaTex (smfart.sty

A Note on ADE-Spectra in Conformal Field Theory

We demonstrate that certain Virasoro characters (and their linear combinations) in minimal and non-minimal conformal models which admit factorized forms are manifestly related to the ADE series. This permits to extract quasi-particle spectra of a Lie algebraic nature which resembles the features of Toda field theory. These spectra possibly admit a construction in terms of the $W_n$-generators. In the course of our analysis we establish interrelations between the factorized characters related to the parafermionic models, the compactified boson and the minimal models.Comment: 7 pages Late

Thermodynamic Bethe Ansatz with Haldane Statistics

We derive the thermodynamic Bethe ansatz equation for the situation inwhich the statistical interaction of a multi-particle system is governed by Haldane statistics. We formulate a macroscopical equivalence principle for such systems. Particular CDD-ambiguities play a distinguished role in compensating the ambiguity in the exclusion statistics. We derive Y-systems related to generalized statistics. We discuss several fermionic, bosonic and anyonic versions of affine Toda field theories and Calogero-Sutherland type models in the context of generalized statistics.Comment: 21 pages latex+3 figures. minor typos corrected/references adde

On the quantum L -operator for the two-dimensional lattice Toda model

We consider the two-dimensional quantum lattice Toda model for affine and simple Lie algebras of type A. For its known L-operator, the second-order correction in lattice parameter ε is found. It is proved that the equation determining the third-order correction in ε has no solutions. Bibliography: 9 title

On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory

The Bethe equations, arising in description of the spectrum of the dilatation operator for the su(2) sector of the N=4 supersymmetric Yang-Mills theory, are considered in the anti-ferromagnetic regime. These equations are deformation of those for the Heisenberg XXX magnet. It is proven that in the thermodynamic limit roots of the deformed equations group into strings. It is proven that the corresponding Yang's action is convex, which implies uniqueness of solution for centers of the strings. The state formed of strings of length (2n+1) is considered and the density of their distribution is found. It is shown that the energy of such a state decreases as n grows. It is observed that non-analyticity of the left hand side of the Bethe equations leads to an additional contribution to the density and energy of strings of even length. Whence it is concluded that the structure of the anti-ferromagnetic vacuum is determined by the behaviour of exponential corrections to string solutions in the thermodynamic limit and possibly involves strings of length 2.Comment: LaTex, 9 pages, 1 figur