Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 107, Issue 12, Pages 2359-2413Publisher
SPRINGER
DOI: 10.1007/s11005-017-0983-6
Keywords
Painleve equation; Painleve tau-function; Supersymmetric gauge theory; Argyres-Douglas theory; Isomonodromic deformation
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Funding
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through Ministry of Research and Innovation
- INFN Iniziativa Specifica STFI
- INFN Iniziativa Specifica GAST
- National Research Foundation of Korea [PG057401] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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We elucidate the relation between Painleve equations and four-dimensional rank one N = 2 theories by identifying the connection associated with Painleve isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated with gauge theories and by studying the corresponding renormalization group flow. Based on this correspondence, we provide long-distance expansions at various canonical rays for all Painleve tau-functions in terms of magnetic and dyonic Nekrasov partition functions for N = 2 SQCD and Argyres-Douglas theories at self-dual Omega background epsilon(1) + epsilon(2) = 0 or equivalently in terms of c = 1 irregular conformal blocks.
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