Recent advances in non-relativistic quantum gravity

In this talk I will show that Newtonian gravity is not the unique non-relativistic gravity theory that can be defined by taking a limit of (matter coupled) general relativity. I will discuss several extensions of Newtonian gravity including non-relativistic gravity theories involving geometries with a co-dimension 2 foliation and with non-zero torsion. Using these extensions, I will show how a non-relativistic limit of 10D supergravity can be defined giving what we call a minimal supergravity theory, that can be identified with the effective low-energy approximation of a non-relativistic superstring theory. Using this identification I will discuss several aspects of non-relativistic superstring theory using field theory techniques. In particular, I will focus on the T-duality rules.