Conformal field theory of Painlevé VI

By O. Gamayun, N. Iorgov, O. Lisovyy. 2012

190 citations recorded by the source corpus.

A bstractGeneric Painlevé VI tau function τ (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 τ (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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1c3bb0faf64c94253898eecc4d43063d3b66095

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In Geometry and Topology

1. O. Gamayun
2. O. Lisovyy
3. N. Iorgov
4. Alexander V. Kitaev

In Mathematical Physics

1. O. Gamayun
2. O. Lisovyy
3. N. Iorgov
4. Alexander V. Kitaev

Citations in the corpus

• How instanton combinatorics solves Painlevé VI, V and IIIs (2013, background): “The above claim was obtained in [27] by identifying τVI(t) with a chiral correlator 〈OL∞ (∞)OL1 (1)OLt (t)OL0 (0)〉 of Virasoro primary fields indexed by matrices Lν ∈ sl2(C) which are related to monodromy matrices of the auxiliary linear problem for PVI by Mν = exp 2π iLν ∈ SL(2, C).”