Action-angle variables for geodesic motions in Sasaki-Einstein spaces $Y^{p,q}$

Abstract

We use the action-angle variables to describe the geodesic motions in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequency is zero indicating a chaotic behavior when the system is perturbed.

arXiv comment12 pages, to appear in Prog. Theor. Exp. Phys

References in corpus (11)

• Supersymmetric AdS_5 solutions of M-theory
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Chaos in the Gauge/Gravity Correspondence
• Analytic Non-integrability in String Theory
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• Integrability Lost
• Symmetries and Integrability
• Special Killing forms on toric Sasaki-Einstein manifolds
• Complete integrability of geodesic motion in Sasaki-Einstein toric $Y^{p,q}$ spaces
• Integrability of geodesics and action-angle variables in Sasaki-Einstein space $T^{1,1}$

Cited by in corpus (1)

• Integrability of the geodesic flow on the resolved conifolds over Sasaki-Einstein space $T^{1,1}$