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Mosc. Math. J., 2014, Volume 14, Number 1, Pages 39–61 (Mi mmj514)  

This article is cited in 23 scientific papers (total in 23 papers)

Five dimensional gauge theories and vertex operators

Erik Carlssona, Nikita Nekrasovbcda, Andrei Okounkovde

a Simons Center for Geometry and Physics, Stony Brook NY 11794-3636 USA
b Alikhanov Institute of Theoretical and Experimental Physics, Moscow 117218 Russia
c Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette 91440 France
d Kharkevich Institute for Information Transmission Problems, Lab. 5, Moscow 127994 Russia
e Department of Mathematics, Columbia University, New York USA

Abstract: We study supersymmetric gauge theories in five dimensions, using their relation to the $K$-theory of the moduli spaces of torsion free sheaves. In the spirit of the BPS/CFT correspondence the partition function and the expectation values of the chiral, BPS protected observables are given by the matrix elements and more generally by the correlation functions in some $q$-deformed conformal field theory in two dimensions. We show that the coupling of the gauge theory to the bi-fundamental matter hypermultiplet inserts a particular vertex operator in this theory. In this way we get a generalization of the main result of a paper by E.C. and A.O. to $K$-theory. The theory of interpolating Macdonald polynomials is an important tool in our construction.

Key words and phrases: gauge theory, representation theory, symmetric group, $K$-theory, Hilbert scheme, BPS/CFT correspondence.

DOI: https://doi.org/10.17323/1609-4514-2014-14-1-39-61

Full text: http://www.mathjournals.org/.../2014-014-001-003.html
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MSC: 33D52, 14D21
Received: October 18, 2012; in revised form July 6, 2013
Language:

Citation: Erik Carlsson, Nikita Nekrasov, Andrei Okounkov, “Five dimensional gauge theories and vertex operators”, Mosc. Math. J., 14:1 (2014), 39–61

Citation in format AMSBIB
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\by Erik~Carlsson, Nikita~Nekrasov, Andrei~Okounkov
\paper Five dimensional gauge theories and vertex operators
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 1
\pages 39--61
\mathnet{http://mi.mathnet.ru/mmj514}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-1-39-61}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3221946}
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    11. Yu. Tachikawa, “A review on instanton counting and W-algebras”, New dualities of sypersymmetric gauge theories, Math. Phys. Stud., Springer, Cham, 2016, 79–120  crossref  mathscinet  zmath  isi
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    19. E. M. Rains, S. O. Warnaar, “A Nekrasov-Okounkov formula for Macdonald polynomials”, J. Algebr. Comb., 48:1 (2018), 1–30  crossref  mathscinet  zmath  isi  scopus
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