In the Thermodynamic Bethe Ansatz approach to 2D integrable, ADE-related quantum field theories one derives a set of algebraic functional equations (a Y-system) which play a prominent role. This set of equations is mapped into the problem of finding finite triangulations of certain 3D manifolds. This mapping allows us to find a general explanation of the periodicity of the Y-system. For the AN related theories and more generally for the various restrictions of the fractionally-supersymmetric sine-Gordon models, we find an explicit, surprisingly simple solution of such functional equations in terms of a single unknown function of the rapidity. The recently-found dilogarithm functional equations associated to the Y-system simply express the invariance of the volume of a manifold for deformations of its triangulations.

Thermodynamic Bethe Ansatz and Threefold Triangulations

GLIOZZI, Ferdinando;TATEO, Roberto
1996-01-01

Abstract

In the Thermodynamic Bethe Ansatz approach to 2D integrable, ADE-related quantum field theories one derives a set of algebraic functional equations (a Y-system) which play a prominent role. This set of equations is mapped into the problem of finding finite triangulations of certain 3D manifolds. This mapping allows us to find a general explanation of the periodicity of the Y-system. For the AN related theories and more generally for the various restrictions of the fractionally-supersymmetric sine-Gordon models, we find an explicit, surprisingly simple solution of such functional equations in terms of a single unknown function of the rapidity. The recently-found dilogarithm functional equations associated to the Y-system simply express the invariance of the volume of a manifold for deformations of its triangulations.
1996
11
4051
4064
http://lanl.arxiv.org/pdf/hep-th/9505102
GLIOZZI F; R. TATEO
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/10275
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