Superintegrability of geodesic motion on the sausage model*This paper is a tribute to the memory of Prof Petr Kulish. (17th May 2017)

• Record Type: Journal Article
• Authors: Arutyunov, Gleb; Heinze, Martin; Medina-Rincon, Daniel
• Is Part Of: Journal of physics. Volume 50:Number 24(2017)
• Publication Date: 2017-05-17
• Subjects: AdS/CFT correspondence -- integrability -- geodesic Motion -- Fateev sausage model -- integrable deformation -- Hamiltonian mechanics; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa6e0c
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Reduction of the η -deformed sigma model on A d S 5 × S 5 to the two-dimensional squashed sphere ( S 2 ) η can be viewed as a special case of the Fateev sausage model where the coupling constant ν 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 s l ( 2 ) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model.