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arXiv · 1209.3984

Seiberg-Witten equations and non-commutative spectral curves in Liouville theory

Leonid Chekhov·Bertrand Eynard·Sylvain Ribault
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Abstract

We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the stress-energy tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.

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Leonid Chekhov, Bertrand Eynard, Sylvain Ribault. 2012-09-18. Seiberg-Witten equations and non-commutative spectral curves in Liouville theory. https://doi.org/10.1063/1.4792241

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