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Quantum group symmetries and non-local currents in 2D QFT

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Abstract

We construct and study the implications of some new non-local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions, including the sine-Gordon theory and its generalization to affine Toda theory. These non-local currents provide a non-perturbative formulation of the theories. The symmetry algebras correspond to the quantum affine Kac-Moody algebras. TheS-matrices are completely characterized by these symmetries. FormalS-matrices for the imaginary-coupling affine Toda theories are thereby derived. The application of theseS-matrices to perturbed coset conformal field theory is studied. Non-local charges generating the finite dimensional Quantum Group in the Liouville theory are briefly presented. The formalism based on non-local charges we describe provides an algernative to the quantum inverse scattering method for solving integrable quantum field theories in 2d.

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Authors and Affiliations

  1. Service de Physique Théorique de Saclay, F-91191, Gif-sur-Yvette, France

    Denis Bernard

  2. Newman Laboratory of Nuclear Studies, Cornell University, 14853, Ithaca, NY, USA

    André LeClair

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  1. Denis Bernard
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  2. André LeClair
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Communicated by N. Yu. Reshetikhin

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Bernard, D., LeClair, A. Quantum group symmetries and non-local currents in 2D QFT. Commun.Math. Phys. 142, 99–138 (1991). https://doi.org/10.1007/BF02099173

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