String Theory on Lorentzian AdS_3 in Minisuperspace

Details String Theory on Lorentzian AdS_3 in Minisuperspace String Theory on Lorentzian AdS_3 in Minisuperspace

2004-03-08

arxiv.org/abs/hep-th/0403081v3

JHEP 0404 (2004) 025

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, no figures, minor changes, references added

Scientific paper

10.1088/1126-6708/2004/04/025

We investigate string theory on Lorentzian AdS_3 in the minisuperspace approximation. The minisuperspace model reduces to the worldline theory of a scalar particle in the Lorentzian AdS_3. The Hilbert space consists of normalizable wave functions, and we see that the unitarity of the theory (or the self-adjointness of the Hamiltonian) restricts the possible sets of wave functions. The restricted wave functions have the property of probability conservation (or current conservation) across the horizons. Two and three point functions are also computed. In the Euclidean model functional forms of these quantities are restricted by the SL(2,R) symmetry almost uniquely, however, in the Lorentzian model there are several ambiguities left. The ambiguities are fixed by the direct computation of overlaps of wave functions.

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