Conformal field theory of Painlevé VI

Abstract

Generic 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.

24 pages, 1 figure; v3: added refs and minor clarifications, few typos corrected; to appear in JHEP

References in corpus (1)

• A direct proof of AGT conjecture at beta = 1

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