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| Paper IPM / Physic / 11143 |
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The near horizon limit of the extremal BTZ black hole is a
"self-dual orbifold" of AdS3. 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 AdS2 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 AdS2, which is consistent with older ideas about
instabilities in this space. We show how the necessary boundary
conditions eliminating AdS2 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.
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