Introductory Causal Dynamical Triangulation

TL;DR

This paper introduces the foundational concepts of Causal Dynamical Triangulation (CDT), focusing on the exactly solvable 2-D model to serve as an accessible entry point for understanding CDT's methods and principles.

Contribution

It provides an explicit, step-by-step derivation of key results in 2-D CDT, serving as a guide for newcomers and clarifying the approach's core ideas.

Findings

2-D CDT can be solved exactly

Explicit derivations aid understanding of CDT methods

Provides foundational insights for higher-dimensional CDT

Abstract

This report aims to present the main ideas of Regge calculus necessary to understand the basic premise of CDT. Next, the main strategy of the CDT approach is introduced in general terms. The main focus of this report is the 2-D model of CDT. The section on the 2-D model closely follows a single paper (\cite{ambjorn98}). While the 4-D or even 3-D case will behave very differently from the 2-D model, 2-D CDT can be solved exactly, and as such offers a better introductory exposition of CDT's methods. Higher-dimensional CDT requires a lot of computer simulation, and lies outside the scope of this report. All derivations carried out explicitly are the result of the author's independent work in attempting to find and prove how the results presented were obtained by CDT authors. Because these derivations were made explicit by the author, this paper can act as a guide to those who are new to CDT.