Double quantization of Seiberg-Witten geometry and W-algebras

TL;DR

This paper demonstrates that double quantization of Seiberg-Witten geometry produces W-algebras, linking gauge theory partition functions to algebraic correlators and extending the AGT correspondence.

Contribution

It establishes a new connection between double quantized Seiberg-Witten curves and W-algebras, providing a free field realization and relating partition functions to algebraic correlators.

Findings

Double quantization defines W$(\Gamma)$-algebra currents.

Partition functions are expressed as W-algebra correlators.

Results extend the AGT relation via gauge/quiver duality.

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.