Three-dimensional quantum geometry and black holes

  title={Three-dimensional quantum geometry and black holes},
  author={M'aximo Banados},
We review some aspects of three-dimensional quantum gravity with emphasis in the ‘CFT → Geometry’ map that follows from the BrownHenneaux conformal algebra. The general solution to the classical equations of motion with anti-de Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantisation. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the Bekenstein… 

Three-Dimensional Black Holes and Liouville Field Theory.

diffS 1 ±. Its quantization provides unitary irreducible representations of the Virasoro algebra, in which the state of the black hole becomes primary. To make the quantization complete, holonomies,

Liouville quantum gravity

Notes on black holes and three dimensional gravity

In these notes we review some relevant results on 2+1 quantum gravity. These include the Chern-Simons formulation and its affine Kac-Moody symmetry, the asymptotic algebra of Brown and Henneaux, and

Asymptotic symmetries of three-dimensional black strings

A bstractWe determine a consistent phase space for a theory consisting in the Einstein-Hilbert action coupled to matter fields (dilaton, one-form, two-form) and containing three-dimensional black

On quantization of AdS3 gravity I: semi-classical analysis

A bstractIn this work we explore ideas in quantizing AdS3 Einstein gravity. We start with the most general solution to the 3d gravity theory which respects Brown-Henneaux boundary conditions. These

2 Boundary conditions in Chern – Simons

We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve

Quantum Gravity in Three Dimensions from Higher-Spin Holography

In this thesis, I explore various aspects of quantum gravity in three dimensions from the perspective of higher-spin holography in anti-de Sitter spacetime. The bulk theory is a higher-spin Vasiliev

Geometric actions for three-dimensional gravity

The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the

Holography for bulk states in 3D quantum gravity

: In this work we discuss the holographic description of states in the Hilbert space of (2+1)-dimensional quantum gravity, living on a time slice in the bulk. We focus on pure gravity coupled to



Black Hole Entropy from Conformal Field Theory in Any Dimension

Restricted to a black hole horizon, the “gauge” algebra of surface deformations in general relativity contains a Virasoro subalgebra with a calculable central charge. The fields in any quantum theory

Conformal description of horizon's states

AdS3 black holes and a stringy exclusion principle

The duality relating near-horizon microstates of black holes obtained as orbifolds of a subset of AdS3 to the states of a conformal field theory is analyzed in detail. The SL(2,R)L?SL(2,R)R invariant

Comments on string theory on AdS(3)

We study string propagation on $AdS_3$ times a compact space from an ``old fashioned'' worldsheet point of view of perturbative string theory. We derive the spacetime CFT and its Virasoro and current

Conformal Field Theory, Geometry, and Entropy

In the context of the AdS/CFT correspondence, an explicit relation between the physical degrees of freedom of 2+1d gravity and the stress tensor of 1+1d conformal field theory is exhibited. Gravity

Embeddings of the Virasoro Algebra and Black Hole Entropy

We consider embeddings of the Virasoro algebra into other Virasoro algebras with different central charges. A Virasoro algebra with central charge $c$ (assumed to be a positive integer) and zero mode

Black holes and branes in string theory

This is a set of introductory lecture notes on black holes in string the- ory. After reviewing some aspects of string theory such as dualities, brane solutions, supersymmetric and non-extremal

Quantization of Gauge Systems

This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical


We derive the Kac–Moody algebra and Virasoro algebra in Chern–Simons theory with boundary by using the symplectic reduction method and the Noether procedures.


  • Lett. B180, 89
  • 1986