Generalized Causal Dynamical Triangulations in two dimensions

Abstract

In this thesis we describe a generalization of two-dimensional Causal Dynamical Triangulations (CDT) that relaxes the time-layering condition and was introduced by Jordan. We present two closely related models which we call bubble generalized CDT (gCDT) and spiral gCDT and we set the first steps towards finding an analytical solution to both of the models. After reformulating the method of solving two-dimensional CDT analytically via the transfer matrices, we devise a similar approach for the bubble gCDT model. We perform the first calculations towards building several simplified versions of the model. We then introduce the framework of matrix models in order to formulate the CDT matrix model that was introduced by Benedetti and Henson and present a generalization for spiral gCDT. We finish with a general discussion of other approaches to gCDT in two dimensions.