Asger Cronberg Ipsen

A thesis submitted September 2015 for the degree of Doctor of Philosophy and defended November 13, 2015.

The PhD School of Science
Faculty of Science, Niels Bohr Institute, University of Copenhagen, Denmark

Supervisor:
Jan Ambjørn

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Abstract

Quantum gravity in two dimensions

The topic of this thesis is quantum gravity in 1 + 1 dimensions. We will focus on two formalisms, namely Causal Dynamical Triangulations (CDT) and Dynamical Triangulations (DT). Both theories regularize the gravity path integral as a sum over triangulations. The difference lies in the class of triangulations considered. While the CDT triangulations have a natural Lorentzian structure, in DT the triangulations are Euclidean.

The thesis is built up around three papers, reproduced as Chapter 3, 4 and 6. The outline is as follows: The _rst two chapters provides background material on path integral quantization and the CDT formalism. In Chapter 3 we consider a generalization of CDT (introduced in Ref. [43]) and show that the continuum limit is the same as for plain CDT. This provides evidence for the robustness of the CDT universality class. Chapter 4 provides an analysis of CDT coupled to Yang-Mills theory. In Chapter 5 we review the DT formalism and some basic aspects of Liouville Theory. We put special emphasis on some subtleties of the continuum limit. Finally, Chapter 6 contains a discussion on mixing between geometrical and matter degrees of freedom, when DT is coupled to non-unitary CFTs.

Most of the material in Chapter 1, 2 and 5 is not new, and we attempt to provide relevant references. Chapter 3 and 4 is co-authored with J. Ambj_rn, while Chapter 6 is co-authored with J. Ambj_rn, A. Gorlich and H.-G. Zhang.

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