Shoichi Kanno, Yutaka Matsuo, Hong Zhang
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 ${\mathcal{W}_{1+\infty}}$ algebra which is called SH$^c$ algebra (or degenerate double affine Hecke algebra) in a 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 for Toda field theory.
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http://arxiv.org/abs/1306.1523
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