4.6 Article

q-deformed Painleve τ function and q-deformed conformal blocks

Journal

Publisher

IOP Publishing Ltd
DOI: 10.1088/1751-8121/aa5572

Keywords

Sakai's classification; Nekrasov partition functions; difference Painleve equations; bilinear equations

Funding

  1. Russian Academic Excellence Project [5-100]
  2. NASU-CNRS project [F14-2016]
  3. Young Russian Mathematics
  4. RFBR [15-32-20974]
  5. Russian Science Foundation [14-12-01383]

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We propose the q-deformation of the Gamayun-Iorgov-Lisovyy formula for the Painleve tau function. Namely, we propose the formula for the t function for the q-difference Painleve equation corresponding to the A(7)((1))' surface (and the A(1)((1)) symmetry) in the Sakai classification. In this formula, the tau function equals the series of q-Virasoro Whittaker conformal blocks (equivalently, the Nekrasov partition functions for pure SU(2) 5d theory).

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