Three-Dimensional Gravity Revisited

TL;DR

This paper explores the duality between three-dimensional pure gravity with negative cosmological constant and certain conformal field theories, proposing the monster CFT as a potential dual at the most negative cosmological constant.

Contribution

It identifies specific conditions under which 3D gravity may be dual to holomorphically factorized CFTs, including the monster theory, and analyzes the spectrum and partition functions of these dual theories.

Findings

The dual CFT at the most negative cosmological constant is likely the monster theory.

The energy spectrum of 3D gravity can be exactly determined under certain conditions.

Partition functions for a sequence of dual CFTs can be computed on hyperelliptic Riemann surfaces.

Abstract

We consider the problem of identifying the CFT's that may be dual to pure gravity in three dimensions with negative cosmological constant. The c-theorem indicates that three-dimensional pure gravity is consistent only at certain values of the coupling constant, and the relation to Chern-Simons gauge theory hints that these may be the values at which the dual CFT can be holomorphically factorized. If so, and one takes at face value the minimum mass of a BTZ black hole, then the energy spectrum of three-dimensional gravity with negative cosmological constant can be determined exactly. At the most negative possible value of the cosmological constant, the dual CFT is very likely the monster theory of Frenkel, Lepowsky, and Meurman. The monster theory may be the first in a discrete series of CFT's that are dual to three-dimensional gravity. The partition function of the second theory in the sequence can be determined on a hyperelliptic Riemann surface of any genus. We also make a similar analysis of supergravity.