q-Vertex Operator from 5D Nekrasov Function

Abstract

The five dimensional AGT correspondence implies the connection between the q-deformed Virasoro block and the 5d Nekrasov partition function. In this paper, we determine a q-deformation of the four-point block in the Coulomb gas representation from the 5d Nekrasov function, and obtain an expression of the q-deformed vertex operator. If we use only one kind of the q-vertex operators, one of the insertion points of them must be modified in order to hold the 2d/5d correspondence.

23 pages; v2: a reference added

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Cited by in corpus (11)

• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• A slow review of the AGT correspondence
• On determinant representation and integrability of Nekrasov functions
• $q$-Virasoro modular double and 3d partition functions
• q-Painleve equation from Virasoro constraints
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• On generalized Macdonald polynomials
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• AGT correspondence, (q-)Painlevè equations and matrix models