Generalized Newton-Cartan Geometries for Particles and Strings

Understand

We discuss the generalized Newton-Cartan geometries that can serve as gravitational background fields for particles and strings.

• In order to enable us to define affine connections that are invariant under all the symmetries of the structure group, we describe torsionful geometries with independent torsion tensors.
• A characteristic feature of the non-Lorentzian geometries we consider is that some of the torsion tensors are so-called `intrinsic torsion' tensors that cannot be absorbed in any of the spin connections.
• Setting some components of these intrinsic torsion tensors to zero leads to constraints on the geometry.