`Stringy' Newton-Cartan Gravity

TL;DR

This paper develops a 'stringy' Newton-Cartan gravity framework emphasizing Galilean observers, providing equations of motion for strings and potential extensions, facilitating non-relativistic AdS/CFT applications.

Contribution

It introduces a novel 'stringy' Newton-Cartan gravity model with explicit string dynamics and symmetries, extending previous non-relativistic gravity theories.

Findings

Derived geodesic equations for fundamental strings.

Formulated bulk equations with a symmetric gravitational potential.

Extended framework to include a non-zero cosmological constant.

Abstract

We construct a "stringy" version of Newton-Cartan gravity in which the concept of a Galilean observer plays a central role. We present both the geodesic equations of motion for a fundamental string and the bulk equations of motion in terms of a gravitational potential which is a symmetric tensor with respect to the longitudinal directions of the string. The extension to include a non-zero cosmological constant is given. We stress the symmetries and (partial) gaugings underlying our construction. Our results provide a convenient starting point to investigate applications of the AdS/CFT correspondence based on the non-relativistic "stringy" Galilei algebra.