Chiral geometries of (2+1)-d AdS gravity

TL;DR

This paper investigates half-AdS geometries in (2+1)-dimensional gravity, revealing their relation to BTZ solutions and implications for the factorization of the Chern-Simons path integral.

Contribution

It demonstrates that half-AdS geometries with trivial right-moving connections are diffeomorphic to BTZ geometries with altered parameters, impacting the understanding of the path integral measure.

Findings

Half-AdS geometries relate to BTZ solutions with different parameters.

Over-spinning solutions can lead to naked closed timelike curves.

Chern-Simons path integral measure cannot factorize in a chiral manner for physical states.

Abstract

Pure gravity in (2+1)-dimensions with negative cosmological constant is classically equivalent Chern-Simons gauge theory with gauge group SO(2; 2), which may be realized on chiral and antichiral gauge connections. This paper looks at half-AdS geometries i.e. those with a trivial rightmoving gauge connection while the left-moving connection is a standard (Banados-Teitelboim- Zanelli) BTZ connection. These are shown to be related by diffeomorphism to a BTZ geometry with different mass and angular momentum. Generically this is over-spinning, leading to a naked closed timelike curves. Other closely related solutions are also studied. These results suggest that the measure of the Chern-Simons path integral cannot factorize in a chiral way, if it is to represent a sum over physically sensible states.