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arXiv · 1205.3256

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

Emilio Rubín de Celis·Osvaldo Santillán
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Abstract

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 $AdS_5\times Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.

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Emilio Rubín de Celis, Osvaldo Santillán. 2012-10-10. Massless geodesics in $AdS_5\times Y(p,q)$ as a superintegrable system. https://doi.org/10.1007/jhep09(2012)032

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