# 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}
}
• Published 27 August 2009
• Physics, Mathematics
• arXiv: High Energy Physics - Theory
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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