Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra

Abstract

We study an analog of the AGT relation in five dimensions. We conjecture that the instanton partition function of 5D N=1 pure SU(2) gauge theory coincides with the inner product of the Gaiotto-like state in the deformed Virasoro algebra. In four dimensional case, a relation between the Gaiotto construction and the theory of Braverman and Etingof is also discussed.

12 pages, reference added, minor corrections (typos, notation changes, etc)

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• Norm of the Whittaker vector of the deformed Virasoro algebra
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