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TITLE New quantum toroidal algebras from 5D N=1 instantons on orbifolds
KIAS AUTHORS Bourgine, Jean-Emile
JOURNAL JOURNAL OF HIGH ENERGY PHYSICS, 2020
ARCHIVE arXiv:1906.01625
ABSTRACT Quantum toroidal algebras are obtained from quantum affine algebras by a further affinization, and, like the latter, can be used to construct integrable systems. These algebras also describe the symmetries of instanton partition functions for 5D N = 1 supersymmetric quiver gauge theories. We consider here the gauge theories defined on an orbifold S(1)x C-2/Z(p) where the action of Z(p) is determined by two integer parameters (nu (1), nu (2)). The corresponding quantum toroidal algebra is introduced as a deformation of the quantum toroidal algebra of gl(p). We show that it has the structure of a Hopf algebra, and present two representations, called vertical and horizontal, obtained by deforming respectively the Fock representation and Saito's vertex representations of the quantum toroidal algebra of gl(p). We construct the vertex operator intertwining between these two types of representations. This object is identified with a (nu (1), nu (2))-deformation of the refined topological vertex, allowing us to reconstruct the Nekrasov partition function and the qq-characters of the quiver gauge theories.
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