A Simple Proof of the Chiral Gravity Conjecture

TL;DR

This paper provides a simple proof that at the critical coupling, three-dimensional chiral gravity exhibits only right-moving excitations, confirming its purely chiral nature through symmetry analysis.

Contribution

It demonstrates that at the chiral point, the asymptotic symmetry group reduces to a single right-moving conformal group, establishing the theory's chirality nonperturbatively.

Findings

The group of trivial diffeomorphisms includes left-moving transformations at the chiral point.

The asymptotic symmetry group contains only one (right-moving) conformal group.

Physical excitations are annihilated by left-moving conformal transformations.

Abstract

Chiral gravity is three-dimensional asymptotically AdS3 gravity with an Einstein, cosmological, and Chern-Simons term at a critical value of the coupling denoted \mu\ell=1. Ordinarily, excitations of AdS3 gravity are known to transform non-trivially under an asymptotic symmetry group consisting of both a left-moving and a right-moving conformal group. However it was recently conjectured in arXiv:0801.4566 that at the chiral point \mu\ell=1 all excitations are chiral in that they transform only under the right-moving conformal group. We show herein that at the chiral point, the group of trivial diffeomorphisms is enhanced to include the left-moving conformal transformations, and the asymptotic symmetry group contains only one (right-moving) copy of the conformal group. Diffeomorphism invariance then requires that all physical excitations are annihilated by left-moving conformal transformations, establishing nonperturbatively the chiral nature of chiral gravity.