a Study of Two-Dimensional String Theory
Abstract
This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. There are several chapters. After a general introduction there follows an introduction to the Liouville model where the fundamental issues of its formulation are discussed. In particular the special states are introduced. Then, in chapter three, some calculations of partition functions on genus one are given. These use field theory techniques. The results are compared with the matrix model. In chapter four the matrix model itself is introduced. Some of the concepts and relations which are used in later chapters are explained. Chapters five and six include comments on two important subjects: nonperturbative issues and string theory at finite radius. Chapter seven is devoted to zero momentum correlation functions as calculated in the matrix model. One important result is a set of recursion relations. Chapter eight extends the treatment to nonzero momentum. The main result is a clear identification of the special states. The chapter also includes some comments on the Wheeler de Witt equation. Chapter nine introduces the matrix model W _{infty} algebra. This organizes the results of previous chapters. In particular, a simple derivation of the genus zero tachyon correlation functions is given. Chapter ten extends the results of chapter nine 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, in chapter eleven, the Liouville and matrix model calculations are compared. Finally, chapter twelve is devoted to some general conclusions.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1992
- Bibcode:
- 1992PhDT........75D
- Keywords:
-
- STRING THEORY;
- QUANTUM GRAVITY;
- Physics: Elementary Particles and High Energy