A Non-Relativistic Limit of NS-NS Gravity

TL;DR

This paper explores a specific non-relativistic limit of NS-NS gravity, revealing a new geometric structure called Dilatation invariant String Newton-Cartan geometry, with implications for string theory and gravity.

Contribution

It introduces a non-relativistic limit of NS-NS gravity at the action and equations of motion level, uncovering a novel geometric framework without prior geometric constraints.

Findings

Divergences cancel between Vielbein and Kalb-Ramond terms in the limit.

Emergence of local target space scale invariance in the limit.

Definition of Dilatation invariant String Newton-Cartan geometry.

Abstract

We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.