Massless geodesics in AdS5 × Y (p, q) as a superintegrable system

Abstract

A constant of motion of Carter type for a probe particle in the Y (p, q) EinsteinSasaki backgrounds is presented. This quantity is functionally independent with respect to the five known constants for these geometries. As the metric is five dimensional and the number of independent constants of motion is at least six, the geodesic equations turn out to be superintegrable. This result applies to the configuration of massless geodesic in AdS5 × Y (p, q) studied by Benvenuti and Kruczenski [86], which are matched to long BPS operators in the dual N = 1 supersymmetric gauge theory.