Gauging the Carroll Algebra and Ultra-Relativistic Gravity

It is well known that the geometrical framework of Riemannian geometry that underlies general relativity and its torsionful extension to Riemann-Cartan geometry can be obtained from a procedure known as gauging the Poincare algebra. Recently it has been shown that gauging the centrally extended Galilei algebra, known as the Bargmann algebra, leads to a geometrical framework that when made dynamical gives rise to Horava-Lifshitz gravity. Here we consider the case where we contract the Poincare algebra by sending the speed of light to zero leading to the Carroll algebra. We show how this algebra can be gauged and we construct the most general affine connection leading to the geometry of so-called Carrollian space-times. Carrollian space-times appear for example as the geometry on null hypersurfaces in a Lorentzian space-time of one dimension higher. We also construct theories of ultra-relativistic (Carrollian) gravity in 2+1 dimensions with dynamical exponent z<1 including cases that have anisotropic Weyl invariance for z=0.Comment: 27 page

Dynamics of Carroll Strings

We construct the canonical action of a Carroll string doing the Carroll limit of a canonical relativistic string. We also study the Killing symmetries of the Carroll string, which close under an infinite dimensional algebra. The tensionless limit and the Carroll $p$-brane action are also discussed.Comment: Footnote and references adde

Extended D = 3 Bargmann supergravity from a Lie algebra expansion

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Canonical Analysis of Non-Relativistic Particle and Superparticle

We perform canonical analysis of non-relativistic particle in Newton-Cartan Background. Then we extend this analysis to the case of non-relativistic superparticle in the same background. We determine constraints structure of this theory and find generator of \kappa-symmetry.Comment: 17 pages, references adde

Extended D=3D=3 Bargmann supergravity from a Lie algebra expansion

In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from $D=3$, $\mathcal{N}=2$ superPoincar\'e and its corresponding Chern-Simons supergravity.Comment: 17 page

Remark About Non-Relativistic p-Brane

We define different non-relativistic limit of p-brane with the help of canonical form of the p-brane action. We discuss properties of these actions and their symmetries.Comment: 20 pages, v2:references adde