The final public oral examination of Sameer Murthy will take place on Tuesday, August 3, 2004 at 10:30 a.m. in Room 202. The examining committee will consist of Professors N. Seiberg, H. Verlinde and S. Staggs. Any other members of the University wishing to attend the examination may do so.

The thesis of Sameer Murthy, entitled Closed and Open String Theories in Non-Critical Backgrounds, has been placed on deposit.

Any member of the University wishing to read the thesis may do so. Any objections should be submitted to me in writing. The principal advisor for this work was Prof. Seiberg.

ABSTRACT

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 brane 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.

Daniel Marlow
Chair, Dept. of Physics