Massless geodesics in $AdS_5\times Y(p,q)$ as a superintegrable system

OSVALDO SANTILLÁN; EMILIO RUBÍN DE CELIS

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

Springer

Lugar: Trieste; Año: 2012 vol. 2012 p. 32 - 45

1029-8479

A Carter like constant for the geodesic motion in the $Y(p,q)$ 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 $AdS_5 imes Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.