Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function

TL;DR

This paper derives recursion relations for Nekrasov partition functions in 4D supersymmetric gauge theories, revealing a structure related to deformed W-algebras and conformal Ward identities, advancing the understanding of gauge/CFT correspondence.

Contribution

It introduces an infinite set of recursion formulae for Nekrasov functions based on a deformed W_{1+ finite} algebra, connecting gauge theory partition functions with conformal field theory structures.

Findings

Recursion formulae for Nekrasov partition functions derived.

Identification of algebraic structures with SH^c algebra and W_N algebra.

Connections established between gauge theory and Toda field theory conformal blocks.

Abstract

We derive an infinite set of recursion formulae for Nekrasov instanton partition function for linear quiver U(N) supersymmetric gauge theories in 4D. They have a structure of a deformed version of W_{1+\infty} algebra which is called SH^c algebra (or degenerate double affine Hecke algebra) in the literature. The algebra contains W_N algebra with general central charge defined by a parameter \beta, which gives the $\Omega$ background in Nekrasov's analysis. Some parts of the formulae are identified with the conformal Ward identity for the conformal block function of Toda field theory.