A Study of Two Dimensional String Theory (PhD Thesis)

Abstract

This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. Introductions to both the Liouville model and its matrix model formulation are included. In particular the special states are discussed. Some calculations of partition functions on genus one using field theory techniques are given. Nonperturbative issues and string theory at finite radius are discussed. Zero momentum correlation functions are calculated using the matrix model. One important result is a set of recursion relations. The treatment is extended to nonzero momentum. The main result is a clear identification of the special states. Some comments on the Wheeler de Witt equation is given. The matrix model $W_{\infty }$ algebra is introduced. This organizes the previous results. In particular, a simple derivation of the genus zero tachyon correlation functions is given. The results are then extended to higher genus. It is seen how a deformation of the algebra is responsible for much of the higher genus structure. Some very explicit formulae are derived. Then the Liouville and matrix model calculations are compared followed by some general conclusions.

123 pages. Unix programs "uudecode", "uncompress" and "tar" needed. Instructions included. Uncompressed version available from author

References in corpus (13)

• Evanescent Black Holes
• Applied Conformal Field Theory
• Are Horned Particles the Climax of Hawking Evaporation?
• World Sheet and Space Time Physics in Two Dimensional (Super) String Theory
• Algebraic Structures and Differential Geometry in 2D String Theory
• Exact S-Matrix for 2D String Theory
• Evaporation of Two Dimensional Black Holes
• Gauge Theory Formulation of the $c=1$ Matrix Model: Symmetries and Discrete States
• A Note on Background (In)dependence
• Ward Identities in Two-Dimensional String Theory
• Quantum Rings and Recursion Relations in 2D Quantum Gravity
• $W$-Infinity Ward Identities and Correlation Functions in the $C=1$ Matrix Model
• Puncture Operator in c=1 Liouville Gravity

Cited by in corpus (1)

• Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds