Quantization of Integrable Systems and Four Dimensional Gauge Theories

@article{Nekrasov2010QuantizationOI,
  title={Quantization of Integrable Systems and Four Dimensional Gauge Theories},
  author={Nikita A. Nekrasov and Samson L. Shatashvili},
  journal={arXiv: High Energy Physics - Theory},
  year={2010},
  pages={265-289}
}
We study four dimensional N=2 supersymmetric gauge theory in the Omega-background with the two dimensional N=2 super-Poincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimensional N=2 theory. The epsilon-parameter of the Omega-background is identified with the Planck constant, the twisted chiral ring maps to quantum Hamiltonians, the supersymmetric vacua are identified with… 

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