The Two-Dimensional Stringy Black-Hole: A New Approach and a Pathology

Abstract

The string propagation in the two-dimensional stringy black-hole is investigated from a new approach. We completely solve the classical and quantum string dynamics in the lorentzian and euclidean regimes. In the lorentzian case all the physics reduces to a massless scalar particle described by a Klein-Gordon type equation with a singular effective potential. The scattering matrix is found and it reproduces the results obtained by coset CFT techniques. It factorizes into two pieces : an elastic coulombian amplitude and an absorption part. In both parts, an infinite sequence of imaginary poles in the energy appear. The generic features of string propagation in curved D-dimensional backgrounds (string stretching, fall into spacetime singularities) are analyzed in the present case. A new physical phenomenon specific to the present black-hole is found : the quantum renormalization of the speed of light. We find $c_{quantum} = \sqrt{{k\o{k-2}}}~c_{classical}$, where $k$ is the integer in front of the WZW action. This feature is, however, a pathology. Only for $ k \to \infty$ the pathology disappears (although the conformal anomaly is present). We analyze all the classical euclidean string solutions and exactly compute the quantum partition function. No critical Hagedorn temperature appears here.