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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
Keywords:
orbifolds; density matrix
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