8,336 research outputs found

    q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)

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    We study the properties of one-dimensional hypergeometric integral solutions of the q-difference ("quantum") analogue of the Knizhnik-Zamolodchikov-Bernard equations on tori. We show that they also obey a difference KZB heat equation in the modular parameter, give formulae for modular transformations, and prove a completeness result, by showing that the associated Fourier transform is invertible. These results are based on SL(3,Z) transformation properties parallel to those of elliptic gamma functions.Comment: 39 page

    Restricted Quantum Affine Symmetry of Perturbed Minimal Models

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    We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed sl(2)^\hat{sl(2)} affine Lie algebra symmetry of the sine-Gordon theory can be used to derive the S-matrices of the Φ(1,3)\Phi^{(1,3)} perturbations of the minimal unitary series. This analysis provides an identification of fields which create the massive kink spectrum. We investigate the ultraviolet limit of the restricted sine-Gordon model, and explain the relation between the restriction and the Fock space cohomology of minimal models. We also comment on the structure of degenerate vacuum states. Deformed Serre relations are proven for arbitrary affine Toda theories, and it is shown in certain cases how relations of the Serre type become fractional spin supersymmetry relations upon restriction.Comment: 40 page