Q-deformed Painleve tau function and q-deformed conformal blocks

Abstract

We propose $q$-deformation of the Gamayun-Iorgov-Lisovyy formula for Painlevé $\tau$ function. Namely we propose formula for $\tau$ function for $q$-difference Painlevé equation corresponding to $A_7^{(1)}{}^{\prime }$ surface (and $A_1^{(1)}$ symmetry) in Sakai's classification. In this formula $\tau$ function equals the series of $q$-Virasoro Whittaker conformal blocks (equivalently Nekrasov partition functions for pure $SU(2)$ 5d theory).

21 pages, v2 many typos corrected, references added; v3 several corrections, mainly in App. B; v4 more corrections in App. B

References in corpus (1)

• Fiber-Base Duality and Global Symmetry Enhancement

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