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 [1]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called Ω-background on ℝ4, 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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Correspondence to Nathan Haouzi.

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ArXiv ePrint: 2004.00654

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Haouzi, N., Oh, J. On the quantization of Seiberg-Witten geometry. J. High Energ. Phys. 2021, 184 (2021). https://doi.org/10.1007/JHEP01(2021)184

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Keywords

  • Nonperturbative Effects
  • Supersymmetric Gauge Theory
  • Wilson
  • ’t Hooft and Polyakov loops
  • Quantum Groups