Abstract
We study \( \mathcal{N} \) = 2 supersymmetric gauge theories on the product of a twosphere and a cylinder. We show that the low-energy dynamics of a BPS sector of such a theory is described by a quantum integrable system, with the Planck constant set by the inverse of the radius of the sphere. If the sphere is replaced with a hemisphere, then our system reduces to an integrable system of the type studied by Nekrasov and Shatashvili. In this case we establish a correspondence between the effective prepotential of the gauge theory and the Yang-Yang function of the integrable system.
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ArXiv ePrint: 1310.0827
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Luo, Y., Tan, MC. & Yagi, J. \( \mathcal{N} \) = 2 supersymmetric gauge theories and quantum integrable systems. J. High Energ. Phys. 2014, 90 (2014). https://doi.org/10.1007/JHEP03(2014)090
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DOI: https://doi.org/10.1007/JHEP03(2014)090