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arXiv · 1308.2465

Five dimensional gauge theories and vertex operators

Erik Carlsson·Nikita Nekrasov·Andrei Okounkov
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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 \cite{CO} to $K$-theory. The theory of interpolating Macdonald polynomials is an important tool in our construction.

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Erik Carlsson, Nikita Nekrasov, Andrei Okounkov. 2013-08-12. Five dimensional gauge theories and vertex operators. https://arxiv.org/abs/1308.2465

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