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.

arXiv comment60 pages, 2 figures; v2: some typos corrected, references added

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• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• 5d/6d Wilson loops from blowups
• More on topological vertex formalism for 5-brane webs with O5-plane
• Instanton counting and O-vertex
• Topological strings and Wilson loops
• ABCD of qq-characters
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• New dimer integrable systems and defects in five dimensional gauge theory
• Defects and type D relativistic Toda lattice for some 5d gauge theories
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations