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arXiv · 2004.00654

On the Quantization of Seiberg-Witten Geometry

Nathan Haouzi·Jihwan Oh
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Abstract

We propose a double quantization of four-dimensional ${\cal N}=2$ 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.

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Nathan Haouzi, Jihwan Oh. 2020-04-01. On the Quantization of Seiberg-Witten Geometry. https://doi.org/10.1007/jhep01(2021)184

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