Spinning strings in the $\eta$-deformed Neumann-Rosochatius system

Abstract

The sigma-model of closed strings spinning in the $\eta$-deformation of $Ad{S}_5\times S^5$ leads to an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical system. In this article we construct general solutions to this system that can be written in terms of elliptic functions. The solutions correspond to closed strings with non-constant radii rotating with two different angular momenta in an $\eta$-deformed three-sphere. We analyse the reduction of the elliptic solutions for some limiting values of the deformation parameter. For the case of solutions with constant radii we find the dependence of the classical energy of the string on the angular momenta as an expansion in the 't Hooft coupling.

17 pages. Latex. v2: Additional references. v3: Minor changes and updated references

References in corpus (16)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On deformations of AdS_n x S^n supercosets
• An Integrable Deformation of the AdS5 x S5 Superstring
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Integrability of classical strings dual for noncommutative gauge theories
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Spinning strings in AdS_3 x S^3 with NS-NS flux
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Elliptic solutions in the Neumann-Rosochatius system with mixed flux
• Integrability of the eta-deformed Neumann-Rosochatius model
• Spiky strings in $\varkappa$-deformed $AdS$
• On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Stringy correlations on deformed $Ad{S}_3\times S^3$

Cited by in corpus (1)

• Probing $\eta$ deformed backgrounds with $Dp$ branes