109 research outputs found
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 -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
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