Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Volume 2015, Issue 18, Pages 8903-8924Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rnu209
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Funding
- NSF [DMS-1001777]
- SPbGU [N 11.38.215.2014]
- Ukrainian SFFR [F54.1/019]
- IRSES
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1361856] Funding Source: National Science Foundation
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The short-distance expansion of the tau function of the radial sine-Gordon/Painleve III equation is given by a convergent series which involves irregular c = 1 conformal blocks and possesses certain periodicity properties with respect to monodromy data. The long-distance irregular expansion exhibits a similar periodicity with respect to a different pair of coordinates on the monodromy manifold. This observation is used to conjecture an exact expression for the connection constant providing relative normalization of the two series. Up to an elementary prefactor, it is given by the generating function of the canonical transformation between the two sets of coordinates.
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