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
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.
MSC: 33D52, 14D21
Received: October 18, 2012; in revised form July 6, 2013
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
\by Erik~Carlsson, Nikita~Nekrasov, Andrei~Okounkov
\paper Five dimensional gauge theories and vertex operators
\jour Mosc. Math.~J.
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