Superintegrability of Geodesic Motion on the Sausage Model

@article{Arutyunov2016SuperintegrabilityOG,
  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},
  year={2016}
}
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… Expand

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References

SHOWING 1-10 OF 69 REFERENCES
Coset construction of AdS particle dynamics
We analyze dynamics of the AdS$_{N+1}$ particle realized on the coset SO$(2,N)/$SO$(1,N)$. Hamiltonian reduction provides the physical phase space in terms of the coadjoint orbit obtained by boostingExpand
Target space supergeometry of η and λ-deformed strings
A bstractWe study the integrable η and λ-deformations of supercoset string sigma models, the basic example being the deformation of the AdS5 × S5 superstring. We prove that the kappa symmetryExpand
Derivation of the action and symmetries of the q-deformed AdS5 × S5 superstring
A bstractWe recently proposed an integrable q-deformation of the AdS5 × S5 superstring action. Here we give details on the hamiltonian origin and construction of this deformation. The procedure is aExpand
Supercoset construction of Yang-Baxter deformed AdS$_5\times$S$^5$ backgrounds
We proceed to study Yang-Baxter deformations of the AdS$_5\times$S$^5$ superstring with the classical Yang-Baxter equation. We make a general argument on the supercoset construction and present theExpand
On classical Yang-Baxter based deformations of the AdS5 × S5 superstring
A bstractInteresting deformations of AdS5 × S5 such as the gravity dual of noncommutative SYM and Schödinger spacetimes have recently been shown to be integrable. We clarify questions regarding theExpand
An integrable deformation of the AdS5 × S5 superstring
The S-matrix on the world-sheet theory of the string in AdS has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where qExpand
Puzzles of η-deformed AdS5 × S5
A bstractWe derive the part of the Lagrangian for the sigma model on the η-deformed AdS5 × S5 space which is quadratic in fermions and has the full dependence on bosons. We then show that thereExpand
Quantum deformations of the flat space superstring
We discuss a quantum deformation of the Green-Schwarz superstring on flat space, arising as a contraction limit of the corresponding deformation of AdS_5 x S^5. This contraction limit turns out to beExpand
On integrable deformations of superstring sigma models related to AdSn×Sn supercosets
Abstract We consider two integrable deformations of 2d sigma models on supercosets associated with AdS n × S n . The first, the “η-deformation” (based on the Yang–Baxter sigma model), is aExpand
Generalized type IIB supergravity equations and non-Abelian classical r-matrices
We study Yang-Baxter deformations of the $AdS_5 \times S^5$ superstring with non-Abelian classical $r$-matrices which satisfy the homogeneous classical Yang-Baxter equation (CYBE). By performing aExpand
...
1
2
3
4
5
...