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

TL;DR

This work analyzes the holographic description of near-horizon extremal black holes, showing that the $AdS_2$ throat with electric flux arises as a self-dual orbifold of $AdS_3$ and is dual to a $2d$ CFT subjected to DLCQ. The DLCQ procedure freezes the non-chiral sector, leaving a single chiral Virasoro symmetry and implying no AdS$_2$ dynamics, consistent with stability considerations. The authors connect this to Kerr/CFT, compute the relevant central charge, and argue that chiral CFTs in extremal black hole duals are best understood as DLCQ limits of ordinary $2d$ CFTs, enabling Cardy entropy counting. They discuss two-boundary global versions, AdS$_2$ fragmentation, and directions for explicit bulk–boundary dictionaries and string theory embeddings.

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.