Exceptional Confinement in G(2) Gauge Theory

TL;DR

This study probes confinement in a gauge theory with a centerless group, G(2), showing that color remains confined even though the fundamental representation can be screened by gluons and the string can break. It analyzes G(2) YM, a G(2)–SU(3) Higgs interpolation, QCD-like matter with Majorana quarks, and SUSY extensions, using both analytic arguments and strong-coupling lattice results. A key finding is that confinement can persist without a center-based order parameter, with the Fredenhagen-Marcu observable confirming confinement despite the absence of a nonzero string tension. The work also demonstrates a smooth bridge to ordinary SU(3) confinement via a fundamental Higgs in the {7}, clarifying how center-related phenomena shape (or lose) predictive power for finite-temperature transitions in centerless theories.

Abstract

We study theories with the exceptional gauge group G(2). The 14 adjoint "gluons" of a G(2) gauge theory transform as {3}, {3bar} and {8} under the subgroup SU(3), and hence have the color quantum numbers of ordinary quarks, anti-quarks and gluons in QCD. Since G(2) has a trivial center, a "quark" in the {7} representation of G(2) can be screened by "gluons". As a result, in G(2) Yang-Mills theory the string between a pair of static "quarks" can break. In G(2) QCD there is a hybrid consisting of one "quark" and three "gluons". In supersymmetric G(2) Yang-Mills theory with a {14} Majorana "gluino" the chiral symmetry is Z(4)_χ. Chiral symmetry breaking gives rise to distinct confined phases separated by confined-confined domain walls. A scalar Higgs field in the {7} representation breaks G(2) to SU(3) and allows us to interpolate between theories with exceptional and ordinary confinement. We also present strong coupling lattice calculations that reveal basic features of G(2) confinement. Just as in QCD, where dynamical quarks break the Z(3) symmetry explicitly, G(2) gauge theories confine even without a center. However, there is not necessarily a deconfinement phase transition at finite temperature.

Figures (2)

• Figure 1: The weight diagram of the 7-dimensional fundamental representation of $G(2)$ (rescaled by a factor $\sqrt{2}$).
• Figure 2: The weight diagram of the 14-dimensional adjoint representation of $G(2)$ (rescaled by a factor $\sqrt{2}$).