Massless geodesics in $AdS_5\times Y(p,q)$ as a superintegrable system
High Energy Physics - Theory
2012-10-12 v4 Mathematical Physics
Differential Geometry
Dynamical Systems
math.MP
Abstract
A Carter like constant for the geodesic motion in the Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geodesic equations are superintegrable. We point out that this result applies to the configuration of massless geodesic in studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.
Keywords
Cite
@article{arxiv.1205.3256,
title = {Massless geodesics in $AdS_5\times Y(p,q)$ as a superintegrable system},
author = {Emilio Rubín de Celis and Osvaldo Santillán},
journal= {arXiv preprint arXiv:1205.3256},
year = {2012}
}
Comments
20 pages, no figures. Small misprint is corrected in the Killing-Yano tensor. No change in any result or conclusions