Classification of Conformal Carroll Algebras

Abstract

We classify a one-parameter family, ${\mathfrak{confcarr}}_z(d+1)$, of conformal extensions of the Carroll algebra in arbitrary dimension with $z$ being the anisotropic scaling exponent. We further obtain their infinite-dimensional extensions, ${\widetilde{\mathfrak{confcarr}}}_z(d+1)$, and discuss their corresponding finite-dimensional truncated subalgebras when the scaling exponent is integer or half-integer. For all these conformal extensions, we also constrain the 2-point and 3-point correlation functions with electric and/or magnetic features.

51 pages, v2: references added + few minor corrections and clarifications

References in corpus (39)

• Aspects of the BMS/CFT correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Asymptotic symmetries and subleading soft graviton theorem
• Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Supertranslations and Superrotations at the Black Hole Horizon
• Flat Holography: Aspects of the dual field theory
• Warped Conformal Field Theory
• Conformal Carroll groups
• Soft Heisenberg hair on black holes in three dimensions
• Extended Symmetries at the Black Hole Horizon
• Spacetime structure near generic horizons and soft hair
• Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
• Field Theories with Conformal Carrollian Symmetry
• Most general flat space boundary conditions in three-dimensional Einstein gravity
• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• Magic Fermions: Carroll and Flat Bands
• The BMS4 algebra at spatial infinity
• Near-Horizon Geometry and Warped Conformal Symmetry
• Flat space holography and complex SYK
• Conformal Carroll Scalars with Boosts
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Carroll covariant scalar fields in two dimensions
• Dynamical structure of Carrollian Electrodynamics
• Deforming the Maxwell-Sim Algebra
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Kinematical Lie algebras via deformation theory
• Carroll fermions in two dimensions
• The Symmetries of the Carroll Superparticle
• Non-Lorentzian theories with and without constraints
• On Rigidity of 3d Asymptotic Symmetry Algebras
• Carrollian conformal scalar as flat-space singleton
• Flat JT Gravity and the BMS-Schwarzian
• Interpolating Between Asymptotic and Near Horizon Symmetries
• Higher-dimensional kinematical Lie algebras via deformation theory
• Super-Carrollian and Super-Galilean Field Theories
• A Solvable Model of Flat Space Holography
• Holography in CGHS supergravity

Cited by in corpus (3)

• Anisotropic conformal Carroll field theories and their gravity duals
• Post-Carrollian Mechanics, Ideal Gas, and Gravity
• Scaling Symmetry and Carrollian Gravity