A causal perspective on random geometry
Abstract
In this thesis we investigate the importance of causality in nonperturbative approaches to quantum gravity. Firstly, causal sets are introduced as a simple kinematical model for causal geometry. It is shown how causal sets could account for the microscopic origin of the Bekenstein entropy bound. Holography and finite entropy emerge naturally from the interplay between causality and discreteness. Going beyond causal set kinematics is problematic however. It is a hard problem to find the right amplitude to attach to each causal set that one needs to define the nonperturbative quantum dynamics of gravity. One approach which is ideally suited to define the nonperturbative gravitational path integral is dynamical triangulation. Without causality this method leads to unappealing features of the quantum geometry though. It is shown how causality is instrumental in regulating this pathological behavior. In two dimensions this approach of causal dynamical triangulations has been analytically solved by transfer matrix methods. In this thesis considerable progress has been made in the development of more powerful techniques for this approach. The formulation through matrix models and a string field theory allow us to study interesting generalizations. Particularly, it has become possible to define the topological expansion. A surprising twist of the new matrix model is that it partially disentangles the largeN and continuum limit. This makes our causal model much closer in spirit to the original idea by 't Hooft than the conventional matrix models of noncritical string theory.
 Publication:

Ph.D. Thesis
 Pub Date:
 May 2009
 arXiv:
 arXiv:0905.0213
 Bibcode:
 2009PhDT.......103Z
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Theory
 EPrint:
 230 pages, reduced images, PhD thesis in theoretical physics, Imperial College London (2008)