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\noindent 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.
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