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https://hdl.handle.net/2142/22263
Description
Title
Random surfaces and the Yang-Lee edge singularity
Author(s)
Staudacher, Matthias
Issue Date
1990
Doctoral Committee Chair(s)
Kogut, John B.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Elementary Particles and High Energy
Language
eng
Abstract
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.
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