Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole

TL;DR

This paper reviews how (2+1)-dimensional gravity relates to conformal field theory and explores implications for black hole thermodynamics and quantum mechanics.

Contribution

It provides a comprehensive review of the holographic relationship between 3D gravity and 2D conformal field theories, emphasizing black hole physics.

Findings

Gravity in 3D is a topological field theory.

Holographic duality links 3D gravity to 2D conformal field theory.

Insights into black hole statistical and quantum mechanics.

Abstract

In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by a two-dimensional conformal field theory at the ``boundary'' of spacetime. I review what is known about this reduction--mainly within the context of pure (2+1)-dimensional gravity--and discuss its implications for our understanding of the statistical mechanics and quantum mechanics of black holes.