On representation matrices of boundary conditions in $SU(n)$ gauge theories compactified on two-dimensional orbifolds

Abstract

We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in $SU(n)$ or $U(n)$ gauge theories compactified on the orbifolds $T^2/{\mathbb{Z}}_N$ ($N=2,3,4,6$). We suppose that the theory has a global $G^{\prime }=U(n)$ symmetry. Using constraints, unitary transformations and gauge transformations, we examine whether the representation matrices can simultaneously become diagonal or not. We show that at least one diagonal representative necessarily exists in each equivalence class on $T^2/{\mathbb{Z}}_2$ and $T^2/{\mathbb{Z}}_3$, but the representation matrices on $T^2/{\mathbb{Z}}_4$ and $T^2/{\mathbb{Z}}_6$ can contain not only diagonal matrices but also non-diagonal $2\times 2$ ones and non-diagonal $3\times 3$ and $2\times 2$ ones, respectively, as members of block-diagonal submatrices. These non-diagonal matrices have discrete parameters, which means that the rank-reducing symmetry breaking can be caused by the discrete Wilson line phases.

arXiv comment58 pages, major parts of derivations are moved into the appendices

References in corpus (34)

• Electroweak symmetry breaking from dimensional deconstruction
• Gauge Unification in Higher Dimensions
• Triplet-doublet Splitting, Proton Stability and Extra Dimension
• The Gauge Hierarchy Problem and Higher Dimensional Gauge Theories
• Gauge Symmetry Reduction from the Extra Space $S^1/Z_2$
• Electroweak symmetry breaking and fermion masses from extra dimensions
• Standard Model Higgs from Higher Dimensional Gauge Fields
• The Hosotani Mechanism in Bulk Gauge Theories with an Orbifold Extra Space S^1/Z_2
• Dynamical symmetry breaking in Gauge-Higgs unification on orbifold
• Dynamical Rearrangement of Gauge Symmetry on the Orbifold S^1/Z_2
• Boundary conditions as constraints
• Towards A Realistic Grand Gauge-Higgs Unification
• Gauge-Higgs Unification in Orbifold Models
• Two loop finiteness of Higgs mass and potential in the gauge-Higgs unification
• Two-loop Calculation of Higgs Mass in Gauge-Higgs Unification: 5D Massless QED Compactified on S^1
• Grand Gauge-Higgs Unification
• Gauge-Higgs Grand Unification
• Dynamical Gauge Symmetry Breaking and Mass Generation on the Orbifold T^2/Z_2
• Anomalies in field theories with extra dimensions
• Classification and dynamics of equivalence classes in SU(N) gauge theory on the orbifold $S^1/Z_2$
• A general formula of the effective potential in 5D SU(N) gauge theory on orbifold
• Geometric scaling in high-energy QCD at nonzero momentum transfer
• Geometry of Rank Reduction
• Gauge Symmetry Breaking Patterns in an SU(5) Grand Gauge-Higgs Unification
• The Standard Model Gauge Symmetry from Higher-Rank Unified Groups in Grand Gauge-Higgs Unification Models
• Doublet-Triplet Splitting in an SU(5) Grand Unification
• Higgs as a Probe of Supersymmetric Grand Unification with the Hosotani Mechanism
• Equivalence Classes of Boundary Conditions in Gauge Theory on $Z_3$ Orbifold
• Equivalence Classes of Boundary Conditions in SU(N) Gauge Theory on 2-dimensional Orbifolds
• A New Class of Rank Breaking Orbifolds
• Orbifold family unification using vectorlike representation on six dimensions
• To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification
• Dirac gaugino from grand gauge-Higgs unification
• On diagonal representatives in boundary condition matrices on orbifolds

Cited by in corpus (2)

• Mass spectrum in a six-dimensional $SU(n)$ gauge theory on a magnetized torus
• Trace conservation laws in $T^2/Z_m$ orbifold gauge theories