Gauging the Carroll Algebra and Ultra-Relativistic Gravity

Abstract

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.

27 pages

References in corpus (24)

• Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Galilean Conformal Algebras and AdS/CFT
• Newtonian Gravity and the Bargmann Algebra
• Spacetime Symmetries of the Quantum Hall Effect
• Lifshitz Solutions of D=10 and D=11 supergravity
• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Dynamics of Carroll Particles
• Lifshitz Space-Times for Schroedinger Holography
• Warped Conformal Field Theory as Lower Spin Gravity
• Constructing Lifshitz solutions from AdS
• Holography for Schrodinger backgrounds
• Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
• General coordinate invariance in quantum many-body systems
• Holography for chiral scale-invariant models
• The Symmetries of the Carroll Superparticle
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry
• Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
• Schrodinger Holography for z<2
• Schrödinger Holography with $z=2$

Cited by in corpus (136)

• Flat Holography: Aspects of the dual field theory
• Carrollian Physics at the Black Hole Horizon
• Lifshitz holography
• Carroll contractions of Lorentz-invariant theories
• Carroll Structures, Null Geometry and Conformal Isometries
• Bridging Carrollian and Celestial Holography
• Carroll versus Galilei Gravity
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Perfect Fluids
• Non-Relativistic Gravity and its Coupling to Matter
• Carroll Expansion of General Relativity
• Holographic Reconstruction of 3D Flat Space-Time
• Entanglement Entropy in Warped Conformal Field Theories
• Magic Fermions: Carroll and Flat Bands
• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Carrollian conservation laws and Ricci-flat gravity
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• Conformal Carroll Scalars with Boosts
• Dynamics of Carroll Strings
• Magnetic Carrollian gravity from the Carroll algebra
• Limits of JT gravity
• Spatially isotropic homogeneous spacetimes
• Non-Boost Invariant Fluid Dynamics
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Carrollian hydrodynamics from symmetries
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• On the intrinsic torsion of spacetime structures
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Interacting Conformal Carrollian Theories: Cues from Electrodynamics
• The tensionless path from closed to open strings
• Horizon Shells and BMS-like Soldering Transformations
• Universal Corner Symmetry and the Orbit Method for Gravity
• Carroll black holes
• Carroll covariant scalar fields in two dimensions
• Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Locality and anomalies in warped conformal field theory
• Non-linear black hole dynamics and Carrollian fluids
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Boosting to BMS
• Torsional Newton-Cartan Geometry from the Noether Procedure
• Confined dynamical systems with Carroll or Galilei symmetries
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• A Rindler Road to Carrollian Worldsheets
• Dynamical structure of Carrollian Electrodynamics
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• Unification of Decoupling Limits in String and M-theory
• The Effective Action of Superrotation Modes
• BMS-like symmetries in cosmology
• Extended $D=3$ Bargmann supergravity from a Lie algebra expansion
• Carrollian fluids and spontaneous breaking of boost symmetry
• Carroll fermions in two dimensions
• The Symmetries of the Carroll Superparticle
• Non-Lorentzian theories with and without constraints
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• First order non-Lorentzian fluids, entropy production and linear instabilities
• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum
• Carroll limit of four-dimensional gravity theories in the first order formalism
• Non-Riemannian gravity actions from double field theory
• Carrollian Origin of Spacetime Subsystem Symmetry
• Galilean first-order formulation for the non-relativistic expansion of general relativity
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes
• Carroll versus Galilei from a Brane Perspective
• Quantum Null Geometry and Gravity
• N-extended Chern-Simons Carrollian supergravities in 2+1 spacetime dimensions
• Ideal fracton superfluids
• Gravitation in flat spacetime from entanglement
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• p-brane Newton--Cartan 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 and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Carrollian Yang-Mills Theory
• Ehlers, Carroll, Charges and Dual Charges
• BMS Field Theories and Weyl Anomaly
• Hamiltonian form of `Carroll' gravity
• Quantization of Carrollian conformal scalar theories
• Geometrical tools for embedding fields, submanifolds, and foliations
• Carroll Hawking effect
• Chern-Simons action and the Carrollian Cotton tensors
• Null Dimensional Reduction of M2-Brane
• Carroll membranes
• Carrollian limit of quadratic gravity
• Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Extended Kinematical 3D Gravity Theories
• Stress tensors of 3d Carroll CFTs
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Canonical Analysis of Non-Relativistic Particle and Superparticle
• Torsion and anomalies in the warped limit of Lifschitz theories
• A novel supersymmetric extension of BMS symmetries at null infinity
• Hamiltonian Analysis of Non-Relativistic Non-BPS Dp-brane
• Quantization of Carrollian fermions
• Enstrophy without boost symmetry
• Asymptotic Limit of Null Hypersurfaces
• Setting the connection free in the Galilei and Carroll expansions of gravity
• AdS-Carroll Branes
• Complexity growth of BTZ black hole in massive gravity with a null string
• Remark About Non-Relativistic p-Brane
• Carroll Limit of Non-BPS Dp-Brane
• Holographic entanglement entropy and modular Hamiltonian in warped CFT in the framework of GMMG model
• Asymptotic symmetries of projectively compact order one Einstein manifolds
• Carroll-Schrödinger Equation
• Hydrodynamics in the Carrollian regime
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Note About Integrability of Non-Relativistic String
• Carroll black holes in (A)dS and their higher-derivative modifications
• A discrete discontinuity between the two phases of gravity
• Symmetries and Couplings of Non-Relativistic Electrodynamics
• Asymptotic symmetries in Carrollian theories of gravity
• Anisotropic conformal Carroll field theories and their gravity duals
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• Conformal Carrollian Spin-3 Gravity in 3d
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• A twistorial description of BMS symmetries at null infinity
• Unique Carrollian manifolds emerging from Einstein spacetimes
• One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^{\infty }$
• Universal sectors of two-dimensional Carrollian CFTs
• Post-Carrollian Mechanics, Ideal Gas, and Gravity
• Possible ambient kinematics
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
• Revisiting the Carrollian Scalar Field
• Scaling Symmetry and Carrollian Gravity
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• The gauging procedure and carrollian gravity
• Yang-Mills model for centrally extended 2d gravity
• A non-lorentzian primer