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Lambda<0 Quantum Gravity in 2+1 Dimensions I: Quantum States and Stringy SMatrix  Kirill Krasnov
;  Date: 
18 Dec 2001  Journal:  Class.Quant.Grav. 19 (2002) 39773998  Subject:  hepth grqc  Affiliation:  UCSB  Abstract:  We consider the theory of pure gravity in 2+1 dimensions, with negative cosmological constant. The theory contains simple matter in the form of point particles; the later are classically described as lines of conical singularities. We propose a formalism in which quantum amplitudes for process involving black holes and point particles are obtained as Liouville field theory (LFT) correlation functions on Riemann surfaces X. Point particles are described by LFT vertex operators, black holes (asymptotic regions) are in correspondence with boundaries of X. We analyze two examples: the amplitude for emission of a particle by the BTZ black hole, and the amplitude of black hole creation by two point particles. We then define an inner product between quantum states. The value of this inner product can be interpreted as the amplitude for one set of point particles to go into another set producing black holes. The full particle Smatrix is then given by the sum of all such amplitudes. This Smatrix is that of a noncritical string theory, with the worldsheet CFT being essentially the Liouville theory. Lambda<0 quantum gravity in 2+1 dimensions is thus a string theory.  Source:  arXiv, hepth/0112164  Services:  Forum  Review  PDF  Favorites 


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