11 May 1998 | Juan Maldacena and Andrew Strominger
The paper explores the duality between black holes in $AdS_3$ and conformal field theories (CFTs). The $SL(2,R)_L \otimes SL(2,R)_R$ invariant vacuum on $AdS_3$ corresponds to the NS-NS vacuum of the CFT. Orbifolding $AdS_3$ produces a density matrix with temperature and entropy matching 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 central charge. An upper bound on the BPS particle number follows from the upper bound on the $U(1)$ charge of chiral primaries, which is a stringy exclusion principle not visible in perturbation theory about $AdS_3$. The paper also discusses the relationship between the orbifold procedure and the density matrix of the CFT, and the correspondence between states in $AdS_3$ and the CFT. The NS-NS sector of the CFT is analyzed, showing that chiral primaries correspond to multi-particle BPS states in string theory. The Virasoro generators on $AdS_3$ are discussed, and the RR sector is briefly mentioned.The paper explores the duality between black holes in $AdS_3$ and conformal field theories (CFTs). The $SL(2,R)_L \otimes SL(2,R)_R$ invariant vacuum on $AdS_3$ corresponds to the NS-NS vacuum of the CFT. Orbifolding $AdS_3$ produces a density matrix with temperature and entropy matching 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 central charge. An upper bound on the BPS particle number follows from the upper bound on the $U(1)$ charge of chiral primaries, which is a stringy exclusion principle not visible in perturbation theory about $AdS_3$. The paper also discusses the relationship between the orbifold procedure and the density matrix of the CFT, and the correspondence between states in $AdS_3$ and the CFT. The NS-NS sector of the CFT is analyzed, showing that chiral primaries correspond to multi-particle BPS states in string theory. The Virasoro generators on $AdS_3$ are discussed, and the RR sector is briefly mentioned.