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Geometry of the isotropic oscillator driven by the conformal mode
Geometrization of a Lagrangian conservative system typically amounts to
reformulating its equations of motion as the geodesic equations in a properly
chosen curved spacetime. The conventional methods include the Jacobi metric and
the Eisenhart lift. In this work, a modification of the Eisenhart lift is
proposed which describes the isotropic oscillator in arbitrary dimension driven
by the one-dimensional conformal mode.Comment: V3: 10 pages, presentation improved, the version to appear in Eur.
Phys. J.
Newton-Cartan supergravity with torsion and Schr\"odinger supergravity
We derive a torsionfull version of three-dimensional N=2 Newton-Cartan
supergravity using a non-relativistic notion of the superconformal tensor
calculus. The "superconformal" theory that we start with is Schr\"odinger
supergravity which we obtain by gauging the Schr\"odinger superalgebra. We
present two non-relativistic N=2 matter multiplets that can be used as
compensators in the superconformal calculus. They lead to two different
off-shell formulations which, in analogy with the relativistic case, we call
"old minimal" and "new minimal" Newton-Cartan supergravity. We find
similarities but also point out some differences with respect to the
relativistic case.Comment: 30 page
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