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arXiv · hep-th/9310197

The WZNW model as an integrable perturbation of the Witten conformal point

Oleg A. Soloviev
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Abstract

We show that the WZNW model with arbitrary $σ$-model coupling constant may be viewed as a $σ$-model perturbation of the WZNW theory around the Witten conformal point. In order for the $σ$-model perturbation to be relevant, the level $k$ of the underlying affine algebra has to be negative. We prove that in the large $|k|$ limit the perturbed WZNW system with negative $k$ flows to the conformal WZNW model with positive level. The flow appears to be integrable due to the existence of conserved currents satisfying the Lax equation. This fact is in a favorable agreement with the integrability of the WZNW model discovered by Polyakov and Wiegmann within the Bethe ansatz technique.

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Oleg A. Soloviev. 1993-10-31. The WZNW model as an integrable perturbation of the Witten conformal point. https://doi.org/10.1016/0370-2693(94)90258-5

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