We present an exact one-parameter family of solutions to the classical graviton-dilaton system in two dimensions. The solution can be identified as a black hole. We present the solution both in a Schwarzschild-like gauge and in the target space conformal gauge. We discuss possible relations with matrix models.

We construct supergravity solutions that correspond to N Dp-branes coinciding with N Dp-branes. We study the physical properties of the solutions and analyze the supergravity description of tachyon condensation. We construct an interpolation between the brane-antibrane solution and the Schwarzschild solution and discuss its possible application to the study of non-supersymmetric black holes.

We further study the nonperturbative formulation of two-dimensional black holes. We find a nonlinear differential equation satisfied by the tachyon in the black hole background. We show that singularities in the tachyon field configurations are always associated with divergent semiclassical expansions and are absent in the exact theory. We also discuss how the Euclidian black hole emerges from an analytically continued fermion theory that corresponds to the right side up harmonic oscillator potential.⋆ adhar@tifrvax.bitnet.† mandal@tifrvax.bitnet. ‡ wadia@tifrvax.bitnet

We apply the method of coadjoint orbits of W∞-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space distribution of the Fermi fluid. The action has an infinite series of expansion in the string coupling, which to leading order reduces to the previously discussed geometric action for the classical Fermi fluid based on the group w∞ of area-preserving diffeomorphisms. We briefly discuss the strong coupling limit of the string theory which, unlike the weak coupling regime, does not seem to admit a two-dimensional space-time picture. Our methods are equally applicable to interacting fermions in one dimension.