Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state

TL;DR

This paper explores the five-dimensional SU(2) AGT conjecture, proposing a recursive formula for the deformed Gaiotto state and showing its relation to the Nekrasov partition function, thus reducing the conjecture to this recursion.

Contribution

It introduces a conjectural recursive formula for the inner product of the deformed Gaiotto state and links it to the Nekrasov partition function in five dimensions.

Findings

Recursive formula for the deformed Gaiotto state is proposed.

The Nekrasov partition function satisfies the same recursion.

The AGT conjecture is reduced to this recursive relation.

Abstract

This note deals with the five-dimensional pure SU(2) AGT conjecture proposed by Awata and Yamada. We give a conjecture on a recursive formula for the inner product of the deformed Gaiotto state. We also show that the K-theoretic pure SU(2) Nekrasov partition function satisfies the same recursion relation. Therefore the five-dimensional AGT conjecture is reduced to our conjectural recursive formula.