Towards the fundamental spectrum of the Quantum Yang-Mills Theory

TL;DR

This paper investigates the quantum Einstein-Yang-Mills system using Loop Quantum Gravity, revealing improved UV behavior and proposing a method to compute the fundamental spectrum, linking it to Wilsonian renormalization.

Contribution

It introduces a calculational scheme for the quantum Yang-Mills Hamiltonian spectrum within LQG, connecting it to renormalization group concepts and comparing it to classical background results.

Findings

Improved UV behavior in coupled Einstein-Yang-Mills system

Proposed a method to compute the fundamental spectrum of the quantum Hamiltonian

Commented on the relation to pure Yang-Mills theory on classical spacetime

Abstract

In this work we focus on the quantum Einstein-Yang-Mills sector quantised by the methods of Loop Quantum Gravity (LQG). We point out the improved UV behaviour of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact to the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relation of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.