Spectral Observables and Gauge Field Couplings in Causal Dynamical Triangulations

TL;DR

This paper explores spectral observables derived from Laplace-Beltrami operators in triangulations and investigates the simulation of gauge fields coupled to Causal Dynamical Triangulations, highlighting methods and current challenges.

Contribution

It introduces methods to construct spectral observables from discretized Laplace-Beltrami operators and demonstrates how to simulate gauge fields coupled to CDT in various settings.

Findings

Spectral observables can be constructed from triangulations to extract geometric information.

Simulation results for gauge fields coupled to CDT are presented for specific cases.

Current challenges in simulating gauge fields within CDT are discussed.

Abstract

In the first part of this Chapter, we discuss the role of spectral observables, describing possible ways to build them from discretizations of the Laplace--Beltrami operator on triangulations, and how to extract useful geometric information. In the second part, we discuss how to simulate the composite system of gauge fields coupled to CDT for generic groups and dimensions, showing results in some specific case and pointing out current challenges.