Lie Algebra Expansions and Actions for Non-Relativistic Gravity

Abstract

We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method and illustrate its applications by giving several explicit examples. The method can be generalized to include the construction of actions for ultra-relativistic gravity, i.e. Carroll gravity, and non-relativistic supergravity as well.

arXiv comment37 pages, 1 figure; v2: minor editing plus added references

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• Galilean Conformal Algebras and AdS/CFT
• Non-Relativistic Closed String Theory
• Action Principle for Newtonian Gravity
• Carroll versus Galilei Gravity
• `Stringy' Newton-Cartan Gravity
• Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Expanding Lie (super)algebras through abelian semigroups
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• Nonrelativistic String Theory and T-Duality
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• Three-Dimensional Extended Newtonian (Super)Gravity
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Cited by in corpus (43)

• Non-Relativistic Gravity and its Coupling to Matter
• Carroll Expansion of General Relativity
• Relating non-relativistic string theories
• Nonrelativistic String Theory in Background Fields
• Torsional string Newton-Cartan geometry for non-relativistic strings
• Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Carrollian hydrodynamics from symmetries
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Three-dimensional Maxwellian extended Bargmann supergravity
• Three-Dimensional Extended Lifshitz, Schrödinger and Newton-Hooke Supergravity
• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Carroll limit of four-dimensional gravity theories in the first order formalism
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Galilean free Lie algebras
• Geometrizing non-relativistic bilinear deformations
• Carroll versus Galilei from a Brane Perspective
• Three-dimensional non-relativistic extended supergravity with cosmological constant
• Symmetries of post-Galilean expansions
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• p-brane Newton--Cartan Geometry
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Three-dimensional non-relativistic supergravity and torsion
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• A 3+1 formulation of the 1/c expansion of General Relativity
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Non-relativistic limit of gravity theories in the first order formalism
• Torsion and anomalies in the warped limit of Lifschitz theories
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Carroll-Schrödinger Equation
• Hydrodynamics in the Carrollian regime
• Contractions of the Maxwell algebra
• A free Lie algebra approach to curvature corrections to flat space-time
• Conformal Galilean Spin-3 Gravity in 3d
• Boson-fermion algebraic mapping in second quantization