Topological aspects of G2 Yang-Mills theory

TL;DR

This paper explores the topological properties of G2 Yang-Mills theory, including instantons and topological susceptibility, to understand its similarities with QCD and the role of the center in gauge theories.

Contribution

It extends the study of G2 Yang-Mills theory by analyzing its topological features, such as instantons and susceptibility, across different temperature regimes.

Findings

Identification of topological lumps with instanton charge in lattice configurations

Determination of topological susceptibility at various temperatures

Significant response of topological susceptibility to phase transitions

Abstract

Yang-Mills theory and QCD are well-defined for any Lie group as gauge group. The choice G2 is of great interest, as it is the smallest group with trivial center and being at the same time accessible to simulations. This theory has been found to have many properties in common with SU(3) Yang-Mills theory and QCD, permitting to study the role of the center. Herein, these investigations are extended to topological properties of G2 Yang-Mills theory. After giving the instanton construction for G2, topological lumps with instanton topological charge are identified in cooled lattice configurations. The corresponding topological susceptibility is determined in the vacuum and at low and high temperatures, showing a significant response to the phase structure of the theory.