Closed and open string theories in non-critical backgrounds

This thesis is a study of closed and open string theories in low dimensional spacetimes, and the various relations between these theories. In particular, we focus on the theory of the two-dimensional black hole.; We first study closed strings in the background of the Euclidean two-dimensional black hole (SL2( R )/U(1)) tensored with flat space, using the duality relating these theories to non-critical superstrings described by the supersymmetric sine-Liouville interaction on the worldsheet. We point out a subtlety in their geometric interpretation, and clarify the symmetry structure of the theories based on the understanding of these theories as near horizon limits of wrapped NS5-branes. In one such example (cigar x R6 ), we use the brave description to understand the enhancement of the global symmetry in the coset theory from U(1) to SO(3) under which the sine-Liouville and cigar interactions are related. In the same example, a worldsheet description of the moduli space R4/Z2 is presented.; We then study open strings in the topologically twisted Euclidean two-dimensional black hole which is equivalent to noncritical c = 1 bosonic string theory compactified on a circle at self-dual radius. These strings live on D-branes that are extended along the Liouville direction. We present explicit expressions for the disc two- and three-point functions of boundary operators in this theory, as well as the bulk-boundary two-point function. The expressions obtained are divergent because of resonant behavior at self-dual radius. However, these can be regularised and renormalized in a precise way to get finite results. The boundary correlators are found to depend only on the differences of boundary cosmological constants, suggesting a fermionic behaviour. We initiate a study of the open-string field theory localized to the physical states, which leads to an interesting matrix model.; Finally, we present evidence that the worldvolume theory of N unstable D-particles in type IIB superstring theory in two-dimensions is represented by the supersymmetric matrix model of Marinari and Parisi. This identification suggests that the matrix model gives a holographic descriptions of superstrings in a two-dimensional black hole geometry.