'Stringy' Newton-Cartan gravity

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 nonzero 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.