Geometric actions and flat space holography

Abstract

In this paper we perform the Hamiltonian reduction of the action for three-dimensional Einstein gravity with vanishing cosmological constant using the Chern-Simons formulation and Bondi-van der Burg-Metzner-Sachs (BMS) boundary conditions. An equivalent formulation of the boundary action is the geometric action on BMS${}_3$ coadjoint orbits, where the orbit representative is identified as the bulk holonomy. We use this reduced action to compute one-loop contributions to the torus partition function of all BMS${}_3$ descendants of Minkowski spacetime and cosmological solutions in flat space. We then consider Wilson lines in the ISO$(2,1)$ Chern-Simons theory with endpoints on the boundary, whose reduction to the boundary theory gives a bilocal operator. We use the expectation values and two-point correlation functions of these bilocal operators to compute quantum contributions to the entanglement entropy of a single interval for BMS${}_3$ invariant field theories and BMS${}_3$ blocks, respectively. While semi-classically the BMS${}_3$ boundary theory has central charges $c_1=0$ and $c_2=3/G_N$, we find that quantum corrections in flat space do not renormalize $G_N$, but rather lead to a non-zero $c_1$.

arXiv comment61 pages, v2: typo's fixed and ref's added, v3: added comments and improved discussions. Matches version accepted for publication in JHEP

References in corpus (109)

• The World as a Hologram
• The Black Hole in Three Dimensional Space Time
• Entanglement Entropy and Quantum Field Theory
• Aspects of Holographic Entanglement Entropy
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Entanglement entropy and conformal field theory
• Complexity Equals Action
• Quantum corrections to holographic entanglement entropy
• On BMS Invariance of Gravitational Scattering
• Aspects of the BMS/CFT correspondence
• Dimensional Reduction in Quantum Gravity
• Quantum Gravity Partition Functions in Three Dimensions
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Three-Dimensional Gravity Revisited
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Fermionic Localization of the Schwarzian Theory
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions
• The BMS/GCA correspondence
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• A New Cosmological Scenario in String Theory
• Entanglement Entropy at Large Central Charge
• A holographic reduction of Minkowski space-time
• Holography of 3d Flat Cosmological Horizons
• The flat limit of three dimensional asymptotically anti-de Sitter spacetimes
• Three-dimensional quantum geometry and black holes
• One-loop Partition Functions of 3D Gravity
• Flat Holography: Aspects of the dual field theory
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Entropy of three-dimensional asymptotically flat cosmological solutions
• A 2D Stress Tensor for 4D Gravity
• Quantum Computation as Gravity
• Entanglement entropy in Galilean conformal field theories and flat holography
• A Universal Inequality for CFT and Quantum Gravity
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Conformal Carroll groups
• Flat-Space Chiral Gravity
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
• Conformally Soft Photons and Gravitons
• A Resolution of the Cosmological Singularity with Orientifolds
• Time-dependent Orbifolds and String Cosmology
• A theory of reparameterizations for AdS${}_3$ gravity
• Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory
• Higher spin theory in 3-dimensional flat space
• Celestial amplitudes and conformal soft theorems
• Entanglement Entropy in Flat Holography
• BMS Particles in Three Dimensions
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Asymptotically flat spacetimes in three-dimensional higher spin gravity
• Most general flat space boundary conditions in three-dimensional Einstein gravity
• Asymptotic symmetries and dynamics of three-dimensional flat supergravity
• Lightcone Modular Bootstrap and Pure Gravity
• Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity
• Holographic entanglement entropy and gravitational anomalies
• Notes on the BMS group in three dimensions: II. Coadjoint representation
• Coadjoint orbits of the Virasoro algebra and the global Liouville equation
• Entanglement Entropy and Higher Spin Holography in AdS${}_3$
• Stress tensor correlators in three-dimensional gravity
• BMS Modules in Three Dimensions
• Sphere Packing and Quantum Gravity
• Cosmic evolution from phase transition of 3-dimensional flat space
• Flat space physics from AdS/CFT
• Uplifting AdS3/CFT2 to Flat Space Holography
• The BMS Bootstrap
• Geometric actions for three-dimensional gravity
• Variational principle and 1-point functions in 3-dimensional flat space Einstein gravity
• A Grassmann Path From AdS_3 to Flat Space
• One-loop partition function of three-dimensional flat gravity
• Three-dimensional supergravity reloaded
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• Holographic Entanglement and Poincare blocks in three dimensional flat space
• Supersymmetric Extension of Galilean Conformal Algebras
• Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories
• Flat-Space Energy-Momentum Tensor from BMS/GCA Correspondence
• The nuts and bolts of the BMS Bootstrap
• Characters of the BMS Group in Three Dimensions
• On 3d Bulk Geometry of Virasoro Coadjoint Orbits: Orbit invariant charges and Virasoro hair on locally AdS3 geometries
• Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
• Flat space (higher spin) gravity with chemical potentials
• Near horizon dynamics of three dimensional black holes
• Flat Space Limit of (Higher-Spin) Cardy Formula
• Rotating Higher Spin Partition Functions and Extended BMS Symmetries
• Local quantum energy conditions in non-Lorentz-invariant quantum field theories
• Berry Phases on Virasoro Orbits
• Semi-classical BMS${}_3$ blocks and flat holography
• Gravitational anomalies, entanglement entropy, and flat-space holography
• Asymptotically flat spacetimes with BMS${}_3$ symmetry
• Quantization of conical spaces in 3D gravity
• Virasoro Orbits, AdS_3 Quantum Gravity and Entropy
• On Rigidity of 3d Asymptotic Symmetry Algebras
• Spectral Flow in 3D Flat Spacetimes
• Quantizing higher-spin gravity in free-field variables
• Renormalization of gravitational Wilson lines
• Three-dimensional Black Holes and Liouville Field Theory
• Revisiting the asymptotic dynamics of General Relativity on AdS${}_3$
• BMS Characters and Modular Invariance
• Gravitation in flat spacetime from entanglement
• Quantization of BMS${}_3$ orbits: a perturbative approach
• New N=2 SuperBMS${}_3$ algebra and Invariant Dual Theory for 3D Supergravity
• How General Is Holography?
• Linking Past and Future Null Infinity in Three Dimensions
• Late time Wilson lines
• Extended Supersymmetric BMS${}_3$ algebras and Their Free Field Realisations
• Equivalent Dual Theories for 3D N=2 Supergravity
• Supersymmetric Galilean conformal blocks
• Near-Horizon Extremal Geometries: Coadjoint Orbits and Quantization

Cited by in corpus (24)

• AdS${}_3$ gravity and random CFT
• Bridging Carrollian and Celestial Holography
• The Holographic Nature of Null Infinity
• Limits of JT gravity
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• The Effective Action of Superrotation Modes
• Geometric action for extended Bondi-Metzner-Sachs group in four dimensions
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Symmetries of the Black Hole Interior and Singularity Regularization
• Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• Non-Lorentzian Chaos and Cosmological Holography
• Quantizing Carrollian field theories
• The Shadow Formalism of Galilean CFT${}_2$
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• BMS Modular Diaries: Torus one-point function
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• Semi-classical BMS-blocks from the Oscillator Construction
• BMS${}_3$ Mechanics and the Black Hole Interior
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Phase space holography with no strings attached
• Universal sectors of two-dimensional Carrollian CFTs
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Asymptotic Symmetry and Classical holographic dual of $d{S}_3$ supergravity