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

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 o...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2009-12, Vol.161 (2), p.1485-1496
Main Author: Novikov, D. P.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0040-5779
1573-9333
DOI:10.1007/s11232-009-0135-y