\( \mathcal{N} \) = 2 supersymmetric gauge theories and quantum integrable systems

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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.


Supersymmetric gauge theory Bethe Ansatz 


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of PhysicsNational University of SingaporeSingaporeSingapore
  2. 2.International School for Advanced Studies (SISSA)TriesteItaly
  3. 3.INFN, Sezione di TriesteTriesteItaly

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