Superintegrability of Geodesic Motion on the Sausage Model

  title={Superintegrability of Geodesic Motion on the Sausage Model},
  author={G. E. Arutyunov and Martin Heinze and Daniel Medina-Rincon},
  journal={arXiv: High Energy Physics - Theory},
Reduction of the $\eta$-deformed sigma model on ${\rm AdS}_5 \times {\rm S}^5$ to the two-dimensional squashed sphere $({\rm S}^2)_{\eta}$ can be viewed as a special case of the Fateev sausage model where the coupling constant $\nu$ is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the $\mathfrak{sl}(2… 

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