States of a chiral 2d CFT

TL;DR

This paper investigates the duality between a specific AdS_3 spacetime called the self-dual orbifold and a chiral CFT, exploring its boundary states, geometries, and implications for black hole physics.

Contribution

It introduces new geometries asymptotic to the self-dual orbifold, analyzes boundary states of the dual chiral CFT, and discusses potential causal inconsistencies in the duality framework.

Findings

The self-dual orbifold corresponds to an entangled state of two chiral CFTs.

Constructed geometries represent various states, including the ground state of the chiral CFT.

Identified potential causal issues and proposed possible resolutions.

Abstract

We study the dual description of the self-dual orbifold, a locally AdS_3 spacetime which is a circle fibration over AdS_2 and arises as the near-horizon limit of the extreme BTZ black hole. The geometry has two boundaries; we argue that this should correspond to a saddle-point for two copies of a chiral CFT living on these two boundaries in an entangled state. This picture arises naturally in the near-horizon limit, but there is a potential inconsistency with the bulk physics because of causal connections between the boundaries. We discuss a possible resolution of this puzzle. We also construct geometries which asymptotically approach the self-dual orbifold on a single boundary. These geometries (which contain mild singularities) enable us to explore other states of the dual chiral CFT. One of the geometries corresponds to the ground state of this CFT and can be obtained as a particular near-horizon limit of the BTZ M=0 black hole. The self-dual orbifold is a finite temperature version of this geometry.