Five Dimensional Gauge Theories and Vertex Operators

Erik Carlsson, Nikita Nekrasov, Andrei Okounkov
2014 Moscow Mathematical Journal  
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 bifundamental matter
more » ... ltiplet 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.
doi:10.17323/1609-4514-2014-14-1-39-61 fatcat:64hry2wixrguzplb5rgn6ae5ni