correspondence: Instantons at crossroads and gauge origami

Nikita Nekrasov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationproceedings of the conference String-Math, 2015
EditorsWei Song, Bong H. Lian, Si Li, Shing-Tung Yau
PublisherAmerican Mathematical Society
Number of pages63
ISBN (Electronic)9781470442767
ISBN (Print)9781470429515
Publication statusPublished - 2017
Externally publishedYes
Eventproceedings of the conference String-Math, 2015 - Sanya, China
Duration: 31 Dec 20154 Jan 2016

Publication series

NameProceedings of Symposia in Pure Mathematics
ISSN (Print)0082-0717


Conferenceproceedings of the conference String-Math, 2015


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