What is a chiral 2d CFT? And what does it have to do with extremal black holes?

TL;DR

This paper explores the nature of chiral 2D conformal field theories (CFTs) in the context of extremal black holes, analyzing their dual geometries and boundary conditions to clarify their role in black hole physics.

Contribution

It clarifies the relationship between chiral 2D CFTs and extremal black hole horizons, focusing on boundary conditions and asymptotic symmetries in dual geometries.

Findings

The near-horizon geometry of extremal BTZ black holes is a self-dual orbifold of AdS_3.

In these backgrounds, AdS_2 dynamics are suppressed due to boundary conditions.

One Virasoro algebra remains as the asymptotic symmetry group.

Abstract

The near horizon limit of the extremal BTZ black hole is a``self-dual orbifold'' of AdS_3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS_2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS_2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS_2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.