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The 2×2 matrix Schlesinger system and the Belavin-Polyakov-Zamolodchikov system

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Abstract

We show that the Belavin-Polyakov-Zamolodchikov equation of the minimal model of conformal field theory with the central charge c = 1 for the Virasoro algebra is contained in a system of linear equations that generates the Schlesinger system with 2×2 tmatrices. This generalizes Suleimanov’s result on the Painlevé equations. We consider the properties of the solutions, which are expressible in terms of the Riemann theta function.

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  1. Omsk State Technical University, Omsk, Russia

    D. P. Novikov

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 161, No. 2, pp. 191–203, November, 2009.

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Novikov, D.P. The 2×2 matrix Schlesinger system and the Belavin-Polyakov-Zamolodchikov system. Theor Math Phys 161, 1485–1496 (2009). https://doi.org/10.1007/s11232-009-0135-y

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