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What is a chiral 2d CFT? And what does it have to do with extremal black holes? (English) Zbl 1270.81149

Summary: 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83C57 Black holes
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C45 Quantization of the gravitational field
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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