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.

arXiv comment15 pages

References in corpus (24)

• Quantum Gravity at a Lifshitz Point
• Non-Relativistic Closed String Theory
• Newtonian Gravity and the Bargmann Algebra
• Carroll versus Galilei Gravity
• `Stringy' Newton-Cartan Gravity
• Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Nonrelativistic String Theory and T-Duality
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Three-Dimensional Extended Bargmann Supergravity
• Non-relativistic strings and branes as non-linear realizations of Galilei groups
• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Extended Galilean symmetries of non-relativistic strings
• A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
• On the structure of symmetric self-dual Lie algebras
• Non-Relativistic Maxwell Chern-Simons Gravity
• Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory
• Newton-Cartan Gravity and Torsion
• Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
• An Action for Extended String Newton-Cartan Gravity
• Confined dynamical systems with Carroll or Galilei symmetries
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - II: Dynamical Three-Space Theories
• On-shell versus Off-shell Equivalence in 3D Gravity

Cited by in corpus (10)

• String Theory and String Newton-Cartan Geometry
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• Oddity in nonrelativistic, strong gravity
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions