Phase structure and Hosotani mechanism in gauge theories with compact dimensions revisited

Abstract

We investigate the phase structure of SU(3) gauge theory in four and five dimensions with one compact dimension by using perturbative one-loop and PNJL-model-based effective potentials, with emphasis on spontaneous gauge symmetry breaking. When adjoint matter with the periodic boundary condition is introduced, we have rich phase structure in the quark-mass and compact-size space with gauge-symmetry-broken phases, called the $SU(2)\times U(1)$ split and the $U(1)\times U(1)$ re-confined phases. Our result is qualitatively consistent with the recent lattice calculations. When fundamental quarks are introduced in addition to adjoint quarks, the split phase becomes more dominant and larger as a result of explicit center symmetry breaking. We also show that another $U(1)\times U(1)$ phase (pseudo-reconfined phase) with negative vacuum expectation value of Polyakov loop exists in this case. We study chiral properties in these theories and show that chiral condensate gradually decreases and chiral symmetry is slowly restored as the size of the compact dimension is decreased.

37 pages, 26 figures; matches published version

References in corpus (15)

• Volume independence in large Nc QCD-like gauge theories
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Thermodynamics of the PNJL model
• Finite size phase transitions in QCD with adjoint fermions
• Two loop finiteness of Higgs mass and potential in the gauge-Higgs unification
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Lattice Gauge Theory Approach to Spontaneous Symmetry Breaking from an Extra Dimension
• Large-N volume reduction of lattice QCD with adjoint Wilson fermions at weak-coupling
• The quarkynic phase and the Z_{Nc} symmetry
• Effects of Bulk Mass in Gauge-Higgs Unification
• Correlations among discontinuities in QCD phase diagram
• Light scalars in strongly-coupled extra-dimensional theories
• SUSY breaking scales in the gauge-Higgs unification
• Mean-Field Gauge Interactions in Five Dimensions II. The Orbifold
• New Higgs mechanism from the lattice

Cited by in corpus (14)

• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Polyakov loops and the Hosotani mechanism on the lattice
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
• Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition
• Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry
• Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
• Non-perturbative Gauge-Higgs Unification: Symmetries and Order Parameters
• QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry
• On the phase structure of extra-dimensional gauge theories with fermions
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• Symmetry breaking caused by large R-charge