Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra

TL;DR

This paper explores a five-dimensional extension of the AGT conjecture, proposing a connection between 5D gauge theory partition functions and deformed Virasoro algebra structures.

Contribution

It introduces a novel five-dimensional AGT relation conjecture linking 5D N=1 SU(2) gauge theory to the deformed Virasoro algebra, extending previous 4D results.

Findings

Conjecture that 5D instanton partition functions match inner products in deformed Virasoro algebra.

Discussion of the relation between Gaiotto states and Braverman-Etingof theory in 4D.

Proposes a new framework for understanding 5D gauge theories via algebraic structures.

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.