Chern-Simons expectation values and quantum horizons from LQG and the Duflo map
arXiv:1109.5793 · doi:10.1103/PhysRevLett.108.111303
Abstract
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.
5 pages, 2 figures. v2: update of bibliography, correction of typos, virtually identical to published version
References in corpus (6)
- Detailed black hole state counting in loop quantum gravity
- Black hole entropy quantization
- The SU(2) Black Hole entropy revisited
- Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
- Black hole horizons from within loop quantum gravity
- Chern-Simons theory, Stokes' Theorem, and the Duflo map
Cited by in corpus (20)
- Quantization maps, algebra representation and non-commutative Fourier transform for Lie groups
- Gravitational edge modes: From Kac-Moody charges to Poincaré networks
- Quantum gravity kinematics from extended TQFTs
- Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
- Black Holes as Quantum Gravity Condensates
- Geometric temperature and entropy of quantum isolated horizons
- Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity
- Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity
- Horizon entropy with loop quantum gravity methods
- Dynamical evaporation of quantum horizons
- Entropy of Quantum Black Holes
- Non-commutative Fourier transform for the Lorentz group via the Duflo map
- The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
- Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory
- The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons
- Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
- Extensions of the Duflo map and Chern-Simons expectation values
- Coherent state transforms and the Mackey-Stone-Von Neumann theorem
- Quantum surface holonomies for loop quantum gravity and their application to black hole horizons
- New insights in quantum geometry