Analytic continuation of real Loop Quantum Gravity : Lessons from black hole thermodynamics

Abstract

This contribution is devoted to summarize the recent results obtained in the construction of an "analytic continuation" of Loop Quantum Gravity (LQG). By this, we mean that we construct analytic continuation of physical quantities in LQG from real values of the Barbero-Immirzi parameter $\gamma$ to the purely imaginary value $\gamma =\pm i$. This should allow us to define a quantization of gravity with self-dual Ashtekar variables. We first realized in [1] that this procedure, when applied to compute the entropy of a spherical black hole in LQG for $\gamma =\pm i$, allows to reproduce exactly the Bekenstein-Hawking area law at the semi-classical limit. The rigorous construction of the analytic continuation of spherical black hole entropy has been done in [2]. Here, we start with a review of the main steps of this construction: we recall that our prescription turns out to be unique (under natural assumptions) and leads to the right semi-classical limit with its logarithmic quantum corrections. Furthermore, the discrete and $\gamma$-dependent area spectrum of the black hole horizon becomes continuous and obviously $\gamma$-independent. Then, we review how this analytic continuation could be interpreted in terms of an analytic continuation from the compact gauge group $SU(2)$ to the non-compact gauge group $SU(1,1)$ relying on an analysis of three dimensional quantum gravity.

arXiv comment8 pages, 1 figure, Proceedings of Frontiers of Fundamental Physics 2014 - Proceedings of Science (PoS)

References in corpus (6)

• Quantum Geometry and Black Hole Entropy
• Black hole entropy and isolated horizons thermodynamics
• Statistics, holography, and black hole entropy in loop quantum gravity
• Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity
• Horizon entropy with loop quantum gravity methods
• Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

Cited by in corpus (5)

• The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
• Horizon entropy with loop quantum gravity methods
• Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a Cut-off for Quantum Gravity
• Towards self dual Loop Quantum Gravity
• Semi-classical analysis of black holes in Loop Quantum Gravity: Modelling Hawking radiation with volume fluctuations