N=2 supersymmetric gauge theories and quantum integrable systems

Abstract

We study N=2 supersymmetric gauge theories on the product of a two-sphere 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.

24 pages. v2: references added; v3: minor changes, published version

References in corpus (2)

• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$

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