D-Brane Propagation in Two-Dimensional Black Hole Geometries

We study propagation of D0-brane in two-dimensional Lorentzian black hole backgrounds by the method of boundary conformal field theory of SL(2,R)/U(1) supercoset at level k. Typically, such backgrounds arise as near-horizon geometries of k coincident non-extremal NS5-branes, where 1/k measures curvature of the backgrounds in string unit and hence size of string worldsheet effects. At classical level, string worldsheet effects are suppressed and D0-brane propagation in the Lorentzian black hole geometry is simply given by the Wick rotation of D1-brane contour in the Euclidean black hole geometry. Taking account of string worldsheet effects, boundary state of the Lorentzian D0-brane is formally constructible via Wick rotation from that of the Euclidean D1-brane. However, the construction is subject to ambiguities in boundary conditions. We propose exact boundary states describing the D0-brane, and clarify physical interpretations of various boundary states constructed from different boundary conditions. As it falls into the black hole, the D0-brane radiates off to the horizon and to the infinity. From the boundary states constructed, we compute physical observables of such radiative process. We find that part of the radiation to infinity is in effective thermal distribution at the Hawking temperature. We also find that part of the radiation to horizon is in the Hagedorn distribution, dominated by massive, highly non-relativistic closed string states, much like the tachyon matter. Remarkably, such distribution emerges only after string worldsheet effects are taken exactly into account. From these results, we observe that nature of the radiation distribution changes dramatically across the conifold geometry k = 1 (k = 3 for the bosonic case), exposing the ‘string black hole transition’ therein.