@inproceedings{80c2e18be3a3472bae3189a03f62441e,

title = "correspondence: Instantons at crossroads and gauge origami",

abstract = "Gieseker-Nakajima moduli spaces Mk(n) parametrize the charge k noncommutative U(n) instantons on R4 and framed rank n torsion free sheaves ε on CP2 with ch2(ε) = k. We define a generalization Mk(n) of Mk(n), the moduli space of charge k (noncommutative) instantons on origami spacetimes: a union X of (up to six) coordinate complex planes C2 intersecting in C4, the instantons of a collection of four dimensional gauge theories sewn along two dimensional defect surfaces and defect points. We also define several quiver versions Mγk(nn) of Mk(n), motivated by the considerations of sewn gauge theories on orbifolds C4/G. The geometry of the spaces M γk(n), more specifically the compactness of the set of torus-fixed points, for various tori, underlies the non-perturbative Dyson-Schwinger identities recently found to be satisfied by the correlation functions of qq-characters viewed as local gauge invariant operators in the N = 2 quiver gauge theories. The cohomological and K-theoretic operations defined using Mk(n) and their quiver versions as correspondences provide the geometric counterpart of the qq-characters, line and surface defects.",

author = "Nikita Nekrasov",

year = "2017",

doi = "10.1090/pspum/096/01651",

language = "English",

isbn = "9781470429515",

series = "Proceedings of Symposia in Pure Mathematics",

publisher = "American Mathematical Society",

pages = "183--245",

editor = "Wei Song and Lian, {Bong H.} and Si Li and Shing-Tung Yau",

booktitle = "proceedings of the conference String-Math, 2015",

note = "proceedings of the conference String-Math, 2015 ; Conference date: 31-12-2015 Through 04-01-2016",

}