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Superintegrability of geodesic motion on the sausage model
Univ Hamburg, Inst Theoret Phys, Luruper Chaussee 149, D-22761 Hamburg, Germany.;Univ Hamburg, Zentrum Math Phys, Bundesstr 55, D-20146 Hamburg, Germany.;Steklov Math Inst, Moscow, Russia..
Univ Hamburg, Inst Theoret Phys, Luruper Chaussee 149, D-22761 Hamburg, Germany.;Univ Hamburg, Zentrum Math Phys, Bundesstr 55, D-20146 Hamburg, Germany..
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy. KTH Royal Inst Technol, NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden..
2017 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 24, article id 244002Article in journal (Refereed) Published
Abstract [en]

Reduction of the η-deformed sigma model on AdS5 x S5 to the two-dimensional squashed sphere (S2)η can be viewed as a special case of the Fateev sausage model where the coupling constant v 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 sl(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.

Place, publisher, year, edition, pages
2017. Vol. 50, no 24, article id 244002
Keywords [en]
AdS/CFT correspondence, integrability, geodesic Motion, Fateev sausage model, integrable deformation, Hamiltonian mechanics
National Category
Mathematical Analysis Other Physics Topics
Identifiers
URN: urn:nbn:se:uu:diva-326489DOI: 10.1088/1751-8121/aa6e0cISI: 000402553000001OAI: oai:DiVA.org:uu-326489DiVA, id: diva2:1141582
Available from: 2017-09-15 Created: 2017-09-15 Last updated: 2017-09-15Bibliographically approved

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