3 research outputs found
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
We apply the technique of Hamiltonian reduction for the construction of
three-dimensional supersymmetric mechanics specified by the
presence of a Dirac monopole. For this purpose we take the conventional supersymmetric mechanics on the four-dimensional conformally-flat spaces
and perform its Hamiltonian reduction to three-dimensional system. We formulate
the final system in the canonical coordinates, and present, in these terms, the
explicit expressions of the Hamiltonian and supercharges. We show that, besides
a magnetic monopole field, the resulting system is specified by the presence of
a spin-orbit coupling term. A comparison with previous work is also carried
out.Comment: 9 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-w, accepted for
publication in PRD; minor changes in the Conclusion, the Bibliography and the
Acknowledgemen
Massless geodesics in as a superintegrable system
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.Comment: 20 pages, no figures. Small misprint is corrected in the Killing-Yano
tensor. No change in any result or conclusion