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\(\text{AdS}_3\) black holes and a stringy exclusion principle. (English) Zbl 0951.83019
Summary: The duality relating near-horizon microstates of black holes obtained as orbifolds of a subset of \(\text{AdS}_3\) to the states of a conformal field theory is analyzed in detail. The \(\text{SL}(2,\mathbb{R})_L\otimes \text{SL}(2,\mathbb{R})_{\mathbb{R}}\) invariant vacuum on \(\text{AdS}_3\) corresponds to the NS-NS vacuum of the conformal field theory. The effect of the orbifolding is to produce a density matrix, the temperature and entropy of which coincide with the black hole. For string theory examples the spectrum of chiral primaries agrees with the spectrum of multi-particle BPS states for particle numbers less than the order of the central charge. An upper bound on the BPS particle number follows from the upper bound on the \(U(1)\) charge of chiral primaries. This is a stringy exclusion principle which cannot be seen in perturbation theory about \(\text{AdS}_3\).

MSC:
83C57 Black holes
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
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