CFT/Gravity Correspondence on the Isolated Horizon
arXiv:1405.7056 · doi:10.1016/j.nuclphysb.2014.10.002
Abstract
A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localized at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein-Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures.
22 pages, 2 figure; some important passages have been explained more in detail
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- Flux formulation of loop quantum gravity: Classical framework
- Asymptotically de Sitter Universe inside a Schwarzschild black hole
- Horizon entropy with loop quantum gravity methods
- Statistical and entanglement entropy for black holes in quantum geometry
- Kinematical Gravitational Charge Algebra
- Aspects of quantum gravity
- Quantum Error Correction in Loop Quantum Gravity
- A note on electrical and thermodynamic properties of Isolated Horizon