THERMODYNAMIC BETHE-ANSATZ AND 3-FOLD TRIANGULATIONS

In the thermodynamic Bethe ansatz approach to 2D integrable, ADE-relat ed quantum field theories, one derives a set of algebraic functional e quations (a Y system) which play a prominent role. This set of equatio ns is mapped onto the problem of finding finite triangulations of cert ain 3D manifolds. This mapping allows us to find a general explanation of the periodicity of the Y system. For the A(N) related theories, an d more generally for the various restrictions of the fractionally supe rsymmetric sine-Gordon models, we find an explicit, surprisingly simpl e solution of such functional equations in terms of a single unknown f unction of the rapidity. The recently found dilogarithm functional equ ations associated to the Y system simply express the invariance of the volume of a manifold for deformations of its triangulations.