We elucidate the relation between Painlev\'e equations and four-dimensional rank one N=2 theories by identifying the connection associated to Painlev\'e isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated to gauge theories and by studying the corresponding renormalisation group flow. Based on this correspondence we provide long-distance expansions at various canonical rays for all Painlev\'e functions in terms of magnetic and dyonic Nekrasov partition functions for N=2 SQCD and Argyres-Douglas theories at self-dual Omega background ϵ1+ϵ2=0, or equivalently in terms of c=1 irregular conformal blocks.
On Painlevé/gauge theory correspondence / Bonelli, G.; Lisovyy, O.; Maruyoshi, K.; Sciarappa, A.; Tanzini, A.. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 107:12(2017), pp. 2359-2413. [10.1007/s11005-017-0983-6]
On Painlevé/gauge theory correspondence
Bonelli, G.;Maruyoshi, K.;Sciarappa, A.;Tanzini, A.
2017-01-01
Abstract
We elucidate the relation between Painlev\'e equations and four-dimensional rank one N=2 theories by identifying the connection associated to Painlev\'e isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated to gauge theories and by studying the corresponding renormalisation group flow. Based on this correspondence we provide long-distance expansions at various canonical rays for all Painlev\'e functions in terms of magnetic and dyonic Nekrasov partition functions for N=2 SQCD and Argyres-Douglas theories at self-dual Omega background ϵ1+ϵ2=0, or equivalently in terms of c=1 irregular conformal blocks.| File | Dimensione | Formato | |
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