Stringy (Galilei) Newton-Hooke Chern-Simons gravities

Abstract

We construct Chern-Simons gravities in (2 + 1)-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions. In the first case, there is an invariant and non-degenerate bilinear form, however the field equations do not allow to express the spin connections in terms of the dreibeins. In the second case there is no invariant non-degenerate bilinear form. Therefore, in both cases we do not have an ordinary gravity theory. Instead, if we consider the stringy Newton-Hooke algebra with extensions as gauge group we have an invariant non-degenerate metric and from the field equations we express the spin connections in terms of the geometric fields.

Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

“…The simplest case corresponds to N = 1, which is the unextended p-brane Newton-Hooke algebra in D dimensions [35,76]. The case N = 2 gives a higher-dimensional p-brane generalisation of the three-dimensional extended stringy Newton-Hooke algebra [77]. As in the particle case, higher values of N give rise to post-Newtonian extensions of the brane Newton-Hooke algebra.…”

Background field method for nonlinear sigma models in nonrelativistic string theory

“…In[31], string Newton-Cartan geometry in 2+1 dimensions is studied using a Chern-Simons formulation, where some related identities are also discussed.…”

Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra

“…Double extensions have been used to study several NR symmetries in 2+1 dimensions in a unified fashion[28], and to construct extended stringy Galilean symmetries[48].…”