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

M. A. Bershtein; A. I. Shchechkin

doi:10.1088/1751-8121/aa5572

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

Mathematical Physics 2019-01-03 v4 High Energy Physics - Theory math.MP Quantum Algebra Exactly Solvable and Integrable Systems

Authors: M. A. Bershtein , A. I. Shchechkin

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Abstract

We propose $q$ -deformation of the Gamayun-Iorgov-Lisovyy formula for Painlev\'e $\tau$ function. Namely we propose formula for $\tau$ function for $q$ -difference Painlev\'e equation corresponding to $A_7^{(1)}{}'$ 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).

Keywords

q-deformation Painlevé tau function q-difference equations q-Virasoro algebra conformal blocks Nekrasov partition function Sakai classification

Cite

@article{arxiv.1608.02566,
  title  = {Q-deformed Painleve tau function and q-deformed conformal blocks},
  author = {M. A. Bershtein and A. I. Shchechkin},
  journal= {arXiv preprint arXiv:1608.02566},
  year   = {2019}
}

Comments

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

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

Abstract

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