Double quantization of Seiberg-Witten geometry and W-algebras

Abstract

We show that the double quantization of Seiberg-Witten spectral curve for $\Gamma$-quiver gauge theory defines the generating current of W$(\Gamma )$-algebra in the free field realization. We also show that the partition function is given as a correlator of the corresponding W$(\Gamma )$-algebra, which is equivalent to the AGT relation under the gauge/quiver (spectral) duality.

31 pages, contribution to proceedings for 2016 von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, 4-8 July 2016, Charlotte, NC; typos corrected, refs. updated

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