Geometric actions for three-dimensional gravity

Abstract

The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the centrally extended BMS${}_3$ group in the latter case. Dynamical actions that control these solution spaces are usually constructed by starting from the Chern-Simons formulation and imposing all boundary conditions. In this note, an alternative route is followed. We study in detail how to derive these actions from a group-theoretical viewpoint by constructing geometric actions for each of the coadjoint orbits, including the appropriate Hamiltonians. We briefly sketch relevant generalizations and potential applications beyond three-dimensional gravity.

29 pages

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Cited by in corpus (46)

• Quantum Computation as Gravity
• AdS${}_3$ gravity and random CFT
• Bridging Carrollian and Celestial Holography
• A theory of reparameterizations for AdS${}_3$ gravity
• Low-dimensional de Sitter quantum gravity
• The Schwarzian Theory - A Wilson Line Perspective
• Defects in Jackiw-Teitelboim Quantum Gravity
• Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
• Fine Structure of Jackiw-Teitelboim Quantum Gravity
• Towards a bulk description of higher spin SYK
• A BMS-invariant free scalar model
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Geometric actions and flat space holography
• Near horizon dynamics of three dimensional black holes
• 3D Gravity in a Box
• The Effective Action of Superrotation Modes
• Geometric action for extended Bondi-Metzner-Sachs group in four dimensions
• Symmetries of the Black Hole Interior and Singularity Regularization
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Warped Schwarzian theory
• ${\mathrm{BMS}}_3$ invariant fluid dynamics at null infinity
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• $T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS${}_3$ gravity
• Interpolating Between Asymptotic and Near Horizon Symmetries
• A BMS-invariant free fermion model
• Revisiting the asymptotic dynamics of General Relativity on AdS${}_3$
• Quantizing Carrollian field theories
• Complexity and Emergence of Warped ${\text{AdS}}_3$ Space-time from Chiral Liouville Action
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Kinematic space and the orbit method
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• Virasoro Entanglement Berry Phases
• On the Various Extensions of the BMS Group
• Thomas Precession for Dressed Particles
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• BMS${}_3$ Mechanics and the Black Hole Interior
• Systematics of Boundary Actions in Gauge Theory and Gravity
• Probing Wigner Rotations for Any Group
• Phase space holography with no strings attached
• Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited
• Holography in CGHS supergravity
• Berry Phases in the Bosonization of Nonlinear Edge Modes
• A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product
• The massive BMS character in 3D quantum gravity