BMS Particles in Three Dimensions

Abstract

This thesis is devoted to the group-theoretic aspects of three-dimensional quantum gravity on Anti-de Sitter and Minkowskian backgrounds. In particular we describe the relation between unitary representations of asymptotic symmetry groups and gravitational perturbations around a space-time metric. In the asymptotically flat case this leads to "BMS particles", representing standard relativistic particles dressed with gravitational degrees of freedom accounted for by coadjoint orbits of the Virasoro group. Their thermodynamics are described by BMS characters, which coincide with gravitational one-loop partition functions. We also extend these considerations to higher-spin theories and supergravity.

437 pages (including index), 33 figures. Appendix reproduced from arXiv:1512.03353 [hep-th]. v2: minor typos corrected; published in Springer Theses

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• Mixed-symmetry fields in de Sitter space: a group theoretical glance
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• Geometric actions and flat space holography
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• Massless Scalars and Higher-Spin BMS in Any Dimension
• Semi-classical BMS${}_3$ blocks and flat holography
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• Warped Schwarzian theory
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• BMS4 Algebra, Its Stability and Deformations
• Flat JT Gravity and the BMS-Schwarzian
• Gravitation in flat spacetime from entanglement
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• Horizon Strings as 3d Black Hole Microstates
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• Lifshitz symmetry: Lie algebras, spacetimes and particles
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• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
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• Thomas Precession for Dressed Particles
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• Quantum Correction of the Wilson Line and Entanglement Entropy in the Pure AdS${}_3$ Einstein Gravity Theory
• Bulk Locality and Asymptotic Causal Diamonds
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• Semi-classical BMS-blocks from the Oscillator Construction
• Hypergravity in five dimensions
• Probing Wigner Rotations for Any Group
• The Quantum Gravity Disk: Discrete Current Algebra
• Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals
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• BMS type symmetries at null-infinity and near horizon of non-extermal black holes
• Asymptotic symmetries of three dimensional gravity and the membrane paradigm
• Orbital Bifurcations and Shoaling of Cnoidal Waves
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Asymmetric Galilean conformal algebras
• Adiabatic Deformations of Quantum Hall Droplets
• Relation between Symmetry Groups for Asymptotically Flat Spacetimes
• Galilei particles revisited
• Planons and their Carroll-Galilei symmetries
• Near-Horizon Extremal Geometries: Coadjoint Orbits and Quantization
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
• Polyharmonic Green Functions and Nonlocal BMS Transformations of a Free Scalar Field
• Adiabatic Solutions in General Relativity and Boundary Symmetries
• Constructing the Virasoro groups using differential cohomology
• Topological Bifurcations and Reconstruction of Travelling Waves
• Hirota-Satsuma Dynamics as a Non-Relativistic Limit of KdV Equations
• Asymptotic Structure and Bondi-Metzner-Sachs group in General Relativity
• Ab Initio Construction of Poincaré and AdS Particle
• 3-dimensional $\Lambda$-BMS Symmetry and its Deformations
• BMS in higher space-time dimensions and Non-relativistic BMS
• Symmetries and Asymptotically Flat Space
• On deformations and extensions of $\text{Diff}(S^2)$
• Hidden Symmetries in Gravity : Black holes and other minisuperspaces
• $\mathrm{SDiff}(S^2)$ and the orbit method