`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 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.Comment: 44 page

Newtonian Gravity and the Bargmann Algebra

We show how the Newton-Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e., the centrally extended Galilean algebra. In this gauging procedure several curvature constraints are imposed. These convert the spatial (time) translational symmetries of the algebra into spatial (time) general coordinate transformations, and make the spin connection gauge fields dependent. In addition we require two independent Vielbein postulates for the temporal and spatial directions. In the final step we impose an additional curvature constraint to establish the connection with (on-shell) Newton-Cartan theory. We discuss a few extensions of our work that are relevant in the context of the AdS-CFT correspondence.Comment: Latex, 20 pages, typos corrected, published versio

Newton-Cartan gravity revisited

In this research Newton's old theory of gravity is rederived using an algebraic approach known as the gauging procedure. The resulting theory is Newton's theory in the mathematical language of Einstein's General Relativity theory, in which gravity is spacetime curvature. The gauging procedure sheds new light on Newton's theory en makes extensions of the theory easier to obtain. These extensions are stringy applications and an extension with a symmetry we hope to find in the LHC: supersymmetry. These extensions can be used for the so-called holographic principle, in which a theory of quantum gravity is described by a quantum field theory in one spatial dimension less

A New Perspective on Nonrelativistic Gravity

The geometric reformulation of Newton’s gravity is known as Newton–Cartan theory. We compare the traditional derivation of this theory with a new, algebraic derivation, based on the gauging of a centrally extended Galilean symmetry algebra. In this comparison the role of the central charge gauge field will be explained. In particular, we show that the scalar potential following from this procedure coincides with the one given by the theory of Cartan. Our procedure can be generalized to describe other nonrelativistic limits of gravity involving gravitating strings.

3D Newton–Cartan supergravity

We construct a supersymmetric extension of three-dimensional Newton–Cartan gravity by gauging a super-Bargmann algebra. In order to obtain a non-trivial supersymmetric extension of the Bargmann algebra one needs at least two supersymmetries leading to a N = 2 super-Bargmann algebra. Due to the fact that there is a universal Newtonian time, only one of the two supersymmetries can be gauged. The other supersymmetry is realized as a fermionic Stueckelberg symmetry and only survives as a global supersymmetry. We explicitly show how, in the frame of a Galilean observer, the system reduces to a supersymmetric extension of the Newton potential. The corresponding supersymmetry rules can only be defined, provided we also introduce a ‘dual Newton potential’. We comment on the four-dimensional case.