Spectrum of Yang-Mills theory in 3 and 4 dimensions

TL;DR

This paper provides exact solutions to Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions, yielding precise correlation functions and spectra that agree closely with lattice data, demonstrating high accuracy of theoretical methods.

Contribution

It presents the first exact solutions for correlation functions and spectra of Yang-Mills theory in 3 and 4 dimensions using Dyson-Schwinger equations.

Findings

Correlation functions computed with less than 1% error

Spectra match lattice data across dimensions and gauge groups

Theoretical results validate lattice computations

Abstract

We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and comparison with lattice data can be accomplished. The results are in exceedingly good agreement with an error well below 1\%. This extends both to 3 and 4 dimensions and varying the degree of the gauge group. These results provide a strong support to the value of the lattice computations and show once again how precise can be theoretical computations in quantum field theory.