Polyakov loops and the Hosotani mechanism on the lattice

Understand

We explore the phase structure and symmetry breaking in four-dimensional SU(3) gauge theory with one spatial compact dimension on the lattice ($16^3 \times 4$ lattice) in the presence of fermions in the adjoint representation with periodic boundary conditions.

• We estimate numerically the density plots of the Polyakov loop eigenvalues phases, which reflect the location of minima of the effective potential in the Hosotani mechanism.
• We find strong indication that the four phases found on the lattice correspond to SU(3)-confined, SU(3)-deconfined, SU(2) x U(1), and U(1) x U(1) phases predicted by the one-loop perturbative calculation.
• The case with fermions in the fundamental representation with general boundary conditions, equivalent to the case of imaginary chemical potentials, is also found to support the $Z_3$ symmetry breaking in the effective potential analysis.