Confinement: $G_2$ group case

TL;DR

This paper investigates the deconfinement phase transition in $G_2$ gauge theory, a centreless gauge group, using lattice simulations to understand the role of the group’s centre in confinement.

Contribution

It provides the first lattice study of $G_2$ gauge theory at finite temperature, demonstrating a first-order deconfinement transition and analyzing its critical behavior.

Findings

Deconfinement phase transition occurs in $G_2$ gauge theory.

Transition is strongly indicated to be first order.

Results have implications for understanding colour confinement mechanisms.

Abstract

The gauge group being centreless, $G_2$ gauge theory is a good laboratory for studying the role of the centre of the group for colour confinement in Yang-Mills gauge theories. In this paper, we investigate $G_2$ pure gauge theory at finite temperature on the lattice. By studying the finite size scaling of the plaquette, the Polyakov loop and their susceptibilities, we show that a deconfinement phase transition takes place. The analysis of the pseudocritical exponents give strong evidence of the deconfinement transition being first order. Implications of our findings for scenarios of colour confinement are discussed.