Equivalence Classes of Boundary Conditions in Gauge Theory on Z3 Orbifold

Abstract

We study equivalence classes of boundary conditions in a gauge theory on the orbifold T 2 /Z 3 . Orbifold conditions and those gauge transformation properties are given and the gauge equivalence is understood by the Hosotani mechanism. Mode expansions are carried out for six-dimensional Z 3 singlet fields and a Z 3 triplet field, and the one-loop effective potential for Wilson line phases is calculated. * ) In four-dimensional heterotic string models, extra colored Higgs are projected by the Wilson line mechanism. 4) * * * ) See Ref. 7) for the breakdown of gauge symmetry on S 1 /Z 2 by the Hosotani mechanism. †) The six-dimensional extension of Z 3 orbifold was initially introduced into the construction of four-dimensional heterotic string models. 11) at Florida International University on June 2, 2015 http://ptp.oxfordjournals.org/ Downloaded from * ) We take the SU(3) lattice as the unit lattice. On the estimation of physical quantities, we use physical sizes such as e 1 = 2πR and e 2 = 2πRω. at Florida International University on June 2, 2015 http://ptp.oxfordjournals.org/ Downloaded from * ) If fields and their superpartners yield different BCs, the Scherk-Schwarz mechanism can work. 12) at Florida International University on June 2, 2015 http://ptp.oxfordjournals.org/ Downloaded from * ) The dynamical rearrangement of QCD theta parameter was studied in a five-dimensional gauge theory with a mixed Chern-Simons term. 13) at Florida International University on June 2, 2015 http://ptp.oxfordjournals.org/ Downloaded from * ) For convenience, θ 2 is denoted though it is not an independent parameter. Note that the relation θ 0 θ 1 θ 2 = 1 stems from T Φ [Θ 0 ]T Φ [Θ 1 ]T Φ [Θ 2 ] = I. at Florida International University on June 2, 2015 http://ptp.oxfordjournals.org/ Downloaded fromUsing the equivalence relations (2 . 40) and (2 . 41), we can derive the following equivalence relations in the SU (N ) gauge theory:[l p , m p , n p ; l q , m q , n q ; l r , m r , n r ]

Classification of three-generation models on magnetized orbifolds

“…3 Note that their geometrical aspects are discussed [42][43][44] within the context of string theory. In a higher-dimensional field theory, detailed studies have been carried out [45][46][47][48][49][50].…”

Operator analysis of physical states on magnetized T2/ZN orbifolds

“…On two-dimensional torus T 2 (without magnetic flux), not only the simplest Z 2 case, also more complicated twisted orbifolds T 2 /Z N for N = 3, 4, 6 can be constructed [47] and their geometrical aspects are discussed [51][52][53] within the context of string theory. In a higherdimensional field theory, detailed studies of SU(N ) and SO(N ) gauge theory have been carried out [54][55][56][57][58]. Furthermore on T 6 , which has much amount of degrees of freedom compared with T 2 , other complex patterns are possible like T 6 /Z 7 , T 6 /Z 8 , T 6 /Z 12 and so on.…”

CLASSIFICATION OF STANDARD MODEL PARTICLES IN E6ORBIFOLD GRAND UNIFIED THEORIES

“…Basis vectors, representation matrices and their transformation property of T 2 /Z N are summarized in Table 1. [30,31] 5 Note that there is a choice of representation matrices and P 1 for the Z 2 transformation z → e 1 − z is also used in T 2 /Z 4 and T 2 /Z 6 . Fields possess discrete charges relating eigenvalues of representation matrices for Z M transformation.…”