Superintegrability of 5-d Y(p,q) Einstein-Sasaki metrics

EMILIO RUBÍN DE CELIS

Buenos Aires

Congreso; Pan-American Advanced Studies Institute 2012 - Exploring the Terascale and Beyond; 2012

Universidad de Wisconsin-Madison, National Science Foundation and the Department of Energy under OISE Grant No. 1123982. y UBA FCEN Departamento de Física.

A new constant of motion for the Yp,q Einstein-Sasakicmetrics is presented. To achieve this result Killing and Killing-Yano tensors are used to show that Yp,q manifolds admit hidden symmetries. Finally, the corresponding conserved quantity is constructed. In physics literature one finds that the conjugate momenta P_{theta}, P_ø and P_{psi} together with a total angular momentum J-2 and the Hamiltonian H are 5 constants of motion used to integrate the geodesic equations of motion. The new constant is found to be linearly independent to the previous known, so the problem is shown to be superintegrable.