Twistor representation of Jackiw-Teitelboim gravity
arXiv:2003.13887 · doi:10.1088/1361-6382/aba4ba
Abstract
Jackiw-Teitelboim (JT) gravity is a 1+1-dimensional toy model for quantum gravity in four spacetime dimensions. In the absence of matter, JT gravity is a topological field theory and there are no local observables. The introduction of a boundary changes the situation. What was a un-physical gauge direction before turns into a physical boundary degree of freedom (a gravitational edge mode). Starting from the BF formulation of JT gravity, we develop a twistor representation for the boundary charges of JT gravity. We introduce point sources in the bulk and study the coupled gravity plus matter system at the quantum level. Eigenstates of quasi-local energy are built from the tensor product of unitary irreducible representations of SL(2,R). Empty patches of AdS2 are characterised by the continuous series representations, point sources are related to the discrete series. Physical states are constructed by fusing the SL(2,R) representations into an SL(2,R) invariant singlet. The singlet lies in the kernel of the constraints, which are the analogue of the Wheeler-DeWitt equations in the presence of distributional matter sources.
arXiv comment20 pages
References in corpus (45)
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- Black Hole Entropy from Near-Horizon Microstates
- Quantum Geometry and Black Hole Entropy
- The Spectrum in the Sachdev-Ye-Kitaev Model
- The Spin Foam Approach to Quantum Gravity
- A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
- Dilaton Gravity in Two Dimensions
- Local subsystems in gauge theory and gravity
- Remarks on entanglement entropy for gauge fields
- Solving the Schwarzian via the Conformal Bootstrap
- The Statistical Mechanics of the (2+1)-Dimensional Black Hole
- Bi-Local Holography in the SYK Model
- Gauge Invariant Formulations of Lineal Gravity
- An introduction to the SYK model
- Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
- Geometric entropy and edge modes of the electromagnetic field
- The Off-Shell Black Hole
- Edge states in Gravity and Black Hole Physics
- Black hole entropy and isolated horizons thermodynamics
- How the Change in Horizon Area Drives Black Hole Evaporation
- Quantum dilatonic gravity in d = 2,4 and 5 dimensions
- From twistors to twisted geometries
- Why Gauge?
- The Schwarzian Theory - A Wilson Line Perspective
- Towards a 2d QFT Analog of the SYK Model
- An exact quantization of Jackiw-Teitelboim gravity
- Spinor Representation for Loop Quantum Gravity
- Shockwave S-matrix from Schwarzian Quantum Mechanics
- Defects in Jackiw-Teitelboim Quantum Gravity
- Menagerie of AdS boundary conditions
- Fine Structure of Jackiw-Teitelboim Quantum Gravity
- Lorentz-diffeomorphism edge modes in 3d gravity
- New boundary variables for classical and quantum gravity on a null surface
- Fock representation of gravitational boundary modes and the discreteness of the area spectrum
- The many ways of the characteristic Cauchy problem
- Gravitational edge modes: From Kac-Moody charges to Poincaré networks
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity
- Loop expansion and the bosonic representation of loop quantum gravity
- Kinematical Gravitational Charge Algebra
- Conformal boundary conditions, loop gravity and the continuum
- Generating functional for gravitational null initial data
- Discrete gravity as a topological field theory with light-like curvature defects
- Holographic description of boundary gravitons in (3+1) dimensions
- Deformed Heisenberg charges in three-dimensional gravity