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Conformal field theory of Painlevé VI

Abstract : Generic Painlevé VI tau function \tau(t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with c=1. Using AGT combinatorial representation of conformal blocks and determining the corresponding structure constants, we obtain full and completely explicit expansion of \tau(t) near the singular points. After a check of this expansion, we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlevé VI.
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https://hal.archives-ouvertes.fr/hal-00783915
Contributor : Oleg Lisovyy <>
Submitted on : Friday, February 1, 2013 - 11:45:15 PM
Last modification on : Thursday, March 5, 2020 - 5:33:31 PM

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O. Gamayun, N. Iorgov, O. Lisovyy. Conformal field theory of Painlevé VI. Journal of High Energy Physics, Springer, 2012, 2012 (10), pp.038. ⟨10.1007/JHEP10(2012)038⟩. ⟨hal-00783915⟩

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