Conformal Carroll groups

Abstract

Conformal extensions of Levy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labelled by an integer $k$. This framework includes and extends our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups. The relation to Conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by "Carrollian photons". Motion both in the Newton-Cartan and Carroll spaces may be related to that of strings in the Bargmann space.

31 pages, no figures. Minor misprints corrected and clarifications added. To be published in J. Phys. A

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• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• BMS charge algebra
• The BMS/GCA correspondence
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Galilean Conformal Algebras and AdS/CFT
• Thoughts on Tachyon Cosmology
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• Classical and Quantized Tensionless Strings
• Schr"odinger invariance and space-time symmetries
• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• Tensionless Strings and Galilean Conformal Algebra
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• Fermat Principle for spinning light
• Galilean Isometries
• Einstein-Yang-Mills theory : I. Asymptotic symmetries
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• Symmetries of fluid dynamics with polytropic exponent
• Schild's Null Strings in Flat and Curved Backgrounds
• The Principle of Relativity, Kinematics and Algebraic Relations
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Cited by in corpus (103)

• Carrollian Perspective on Celestial Holography
• Carrollian Physics at the Black Hole Horizon
• Carroll Structures, Null Geometry and Conformal Isometries
• Scattering Amplitudes: Celestial and Carrollian
• Bridging Carrollian and Celestial Holography
• Field Theories with Conformal Carrollian Symmetry
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Carroll Expansion of General Relativity
• Magic Fermions: Carroll and Flat Bands
• Carroll symmetry of plane gravitational waves
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• Conformal Carroll Scalars with Boosts
• Carrollian Approach to $1+3$D Flat Holography
• Geometric actions for three-dimensional gravity
• Brown-York charges at null boundaries
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Carroll/fracton particles and their correspondence
• Carrollian hydrodynamics from symmetries
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• 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
• Universal Corner Symmetry and the Orbit Method for Gravity
• Geometric actions and flat space holography
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Carroll covariant scalar fields in two dimensions
• Rindler on the Worldsheet
• Holographic Lorentz and Carroll Frames
• Inhomogeneous Tensionless Superstrings
• Boosting to BMS
• Planar Carrollean dynamics, and the Carroll quantum equation
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• Confined dynamical systems with Carroll or Galilei symmetries
• Vanishing Love of Black Holes in General Relativity: From Spacetime Conformal Symmetry of a Two-dimensional Reduced Geometry
• Infinite towers of supertranslation and superrotation memories
• A Rindler Road to Carrollian Worldsheets
• BMS-like symmetries in cosmology
• The Effective Action of Superrotation Modes
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Carrollian fluids and spontaneous breaking of boost symmetry
• Carroll fermions in two dimensions
• Constructing Carrollian CFTs
• Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• One-Loop Quantum Effects in Carroll Scalars
• Carroll limit of four-dimensional gravity theories in the first order formalism
• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Scaling and conformal symmetries for plane gravitational waves
• Symmetry group at future null infinity I: Scalar theory
• Memory effect, conformal symmetry and gravitational plane waves
• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
• Tractor geometry of asymptotically flat spacetimes
• A BMS-invariant free fermion model
• The Conformal BMS Group
• Galilean Gauge Theories from Null Reductions
• "Conserved charges" of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory
• Kinematic space and the orbit method
• Symmetry group at future null infinity II: Vector theory
• On Symplectic Form for Null Boundary Phase Space
• The Shadow Formalism of Galilean CFT${}_2$
• Galilean contractions of $W$-algebras
• 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
• BMS symmetry, soft particles and memory
• Quantization of Carrollian conformal scalar theories
• Carroll Hawking effect
• Chern-Simons action and the Carrollian Cotton tensors
• Addendum to "Super-GCA from $\mathcal{N}=(2,2)$ super-Virasoro": Super-GCA connection with tensionless strings
• Flat Bands and Compact Localised States: A Carrollian roadmap
• A novel supersymmetric extension of BMS symmetries at null infinity
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Classification of Conformal Carroll Algebras
• Galilean fermions: Classical and quantum aspects
• Quantization of Carrollian fermions
• Complexity growth of BTZ black hole in massive gravity with a null string
• Boundedness of meta-conformal two-point functions in one and two spatial dimensions
• Carroll-Schrödinger Equation
• Supersymmetric Carroll Galileons in Three Dimensions
• Looking for Carroll particles in two time spacetime
• A microscopic analogue of the BMS group
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• Asymptotic dynamics and charges for FLRW spacetimes
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^{\infty }$
• Post-Carrollian Mechanics, Ideal Gas, and Gravity
• A twistorial description of BMS symmetries at null infinity
• Sourced Carrollian Fluids Dual to Black Hole Horizons
• Scaling Symmetry and Carrollian Gravity
• Carrollian superconformal theories and super BMS
• Null infinity as a Killing horizon
• Carrollian Lie Algebroids: Taming Singular Carrollian Geometries
• Using thermodynamics to learn gravitational wave physics
• Revisiting the Carrollian Scalar Field
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT
• Carrollian ${\mathbb{R}}^{\times }$-bundles: Connections and Beyond
• Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
• One-dimensional Carrollian fluids II: $C^1$ blow-up criteria
• Null reduction and dynamical realization of Carrollian conformal symmetries
• Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics