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

Abstract

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.

On quantization of AdS3 gravity I: semi-classical analysis

“…As was discussed in [27], the above scaling decompactifies x + . On the dual 2d CFT this near horizon limit corresponds to performing a Discrete Light-Cone Quantization (DLCQ) [27].…”

“…the Fourier modes of function f − , which are nothing but the conserved charges associated with a chiral-half of a Virasoro algebra generated by the Brown-Henneaux diffeomorphisms [21,22,27]. 8 …”

“…As pointed out in section 4, one should modify our semiclassical microstate proposal a little bit to fit these cases. Moreover, this case can come with compact or noncompact x + , where the two are related through the DLCQ procedure in the dual CFT [27]. Since in this case we are dealing with a single function f − and hence a chiral sector of a Virasoro algebra, it would be a very good test ground for examining the quantization proposals outlined above.…”

Effective Conformal Descriptions of Black Hole Entropy

“…For example, one can use the AdS/CFT correspondence to identify the boundary stress-energy tensor and look at its anomalous transformation properties [79][80][81]. One can also lift the theory to 2+1 dimensions and exploit the known properties of the BTZ black hole [80][81][82]; for the extremal case, this may offer an interesting connection to the extremal Kerr/CFT correspondence described in Section 4.2, and might explain the appearance of a chiral CFT [83]. These approaches are designed rather particularly for the (1 + 1)-dimensional black hole, however, and seem less general than the boundary symmetry method I have focused on in this review.…”

Three dimensional origin of AdS 2 quantum gravity

“…We maintain excitations above the extremal ground state in this limit, in contrast to discussions invoking a strict extremal limit of the BTZ black hole (see eg. [1,2,9,10]). This is significant because we interpret AdS 2 quantum gravity as the dynamical theory of the excitations above the extremal limit.…”