N. Obers, NBI

Title: “Gravity and String Theory between Newton and Einstein”

Abstract: Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including a novel generalisation that includes torsion) has in recent years gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. After a brief introduction, I will talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. By truncating this expansion at subleading order, we obtain the field content and transformation rules of the fields that appear in the action of Newtonian gravity. The equations of motion generalize Newtonian gravity by allowing for the effect of gravitational time dilation due to strong gravitational field. I will also discuss the relevance of non-relativistic geometry in connection to non-relativistric string theory and holography. In particular, I will show that non-relativistic strings and geometry appear in certain limits of the the AdS/CFT correspondence.