Random surfaces and the Yang-Lee edge singularity

In this thesis we will describe recent progress towards a theory of random surfaces relevant to string theory and two-dimensional quantum gravity. After a brief motivational introduction as well as a general outline of the thesis in the first chapter we will discuss in chapter 2 the continuum approach to random surface theory. It originated with the work of Polyakov and involves functionally integrating over internal metrics. We will review a recently devised method to infer the critical exponents of conformal field theories coupled to the fluctuating metric. Chapter 3 explains a complimentary discrete approach involving sums over random graphs which reproduces essentially the results of the continuum methods. The author's main contribution to the field is contained in chapter 4. We reconsider a recently solved Ising model on a random planar graph. The Yang-Lee edge singularity, familiar from the ordinary Ising model, is exposed. It is shown to correspond to an exactly solvable critical dimer counting problem on the random surface in the infinite temperature limit. The results lead to a deepened insight into the problem of coupling minimal conformal field theories to random surfaces. In chapter 5 we will briefly outline a suggestion on how to obtain and sum the topological expansion of random surfaces. Chapter 6 concludes with a summary of our presentation and results and with pointing at some of the open problems in the field.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Staudacher, Matthias

Contributors dc:contributor

• Kogut, John B.

• Physics, Elementary Particles and High Energy

Statement dc:rights

• Copyright 1990 Staudacher, Matthias

Language dc:language

eng

Identifier

AAI9114422
(UMI)AAI9114422

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/22263