On the Quantization of Seiberg-Witten Geometry

Abstract

We propose a double quantization of four-dimensional $\mathcal{N}=2$ Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by Nekrasov [arXiv:1512.05388]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called $\Omega$-background on ${\mathbb{R}}^4$, in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.

60 pages, 2 figures; v2: some typos corrected, references added