Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function

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.