Spectral Methods in Causal Dynamical Triangulations

TL;DR

This paper explores how spectral analysis of the Laplace-Beltrami operator on spatial slices in Causal Dynamical Triangulations offers insights into the theory's scale behavior and phase transitions, aiding understanding of quantum gravity.

Contribution

It introduces the application of spectral analysis to CDT, revealing new information about the theory's critical behavior and continuum limit implications.

Findings

Eigenvalues indicate scale behavior of the quantum geometry

Spectral analysis reveals critical points in the phase diagram

Results suggest potential continuum limit scenarios

Abstract

We show recent results of the application of spectral analysis in the setting of the Monte Carlo approach to Quantum Gravity known as Causal Dynamical Triangulations (CDT), discussing the behavior of the lowest lying eigenvalues of the Laplace-Beltrami operator computed on spatial slices. This kind of analysis provides information about running scales of the theory and about the critical behaviour around a possible second order transition in the CDT phase diagram, discussing the implications for the continuum limit.