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

Abstract

We construct finite- and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These algebras are also shown to be embedded in different affine Kac-Moody algebras. In the three-dimensional case, we construct Chern-Simons actions invariant under these symmetries. This leads to a sequence of non-relativistic gravity theories, where the simplest examples correspond to extended Newton-Hooke and extended (post-)Newtonian gravity together with their Carrollian counterparts.

35 pages. v2: Small corrections. Published in JHEP

References in corpus (14)

• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Expanding Lie (super)algebras through abelian semigroups
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Relating non-relativistic string theories
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• Extended Galilean symmetries of non-relativistic strings
• A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
• Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra
• Galilean free Lie algebras
• Carroll membranes

Cited by in corpus (41)

• Carroll contractions of Lorentz-invariant theories
• Non-Relativistic Gravity and its Coupling to Matter
• Carroll Expansion of General Relativity
• Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity
• Limits of JT gravity
• Carrollian hydrodynamics from symmetries
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes
• Three-dimensional Maxwellian extended Bargmann supergravity
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Carroll versus Galilei from a Brane Perspective
• Three-dimensional non-relativistic extended supergravity with cosmological constant
• Symmetries of post-Galilean expansions
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Three-dimensional non-relativistic supergravity and torsion
• Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions
• Carroll Hawking effect
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Extended Kinematical 3D Gravity Theories
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Non-relativistic gravity theories in four spacetime dimensions
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• A free Lie algebra approach to curvature corrections to flat space-time
• Carroll-Schrödinger Equation
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Asymptotic symmetries in Carrollian theories of gravity
• Universal sectors of two-dimensional Carrollian CFTs
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• Three-dimensional non-relativistic Hietarinta supergravity
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions