171ZN orbifold models which have N=1 space-time supersymmetry are examined. All gauge groups of ZN orbifold models are classified completely. § 1. IntroductionThe E8 x E8 heterotic string theoryl) has drawn much attention as the unified theory of all known interactions. But it is ten-dimensional theory and has urirealistic gauge group E8XE8 with no matter field. We need several compactification schemes to lead to a four-dimensional theory. T~ toroidal compactification, which is the simplest way to reduce space-time dimensions, however, leads to· four-dimensional theory with N=4 space-time supersymmetry.To obtain four-dimensional theory with N=1 space-time supersymmetry, more realistic gauge group and matters, one of the most interesting ideas is the ZN orbifold compactification.2 ) The ZN orbifold is the quotient of an extra six-dimensional torus T6 divided by a discrete rotation. It has been known that orders N of the discrete rotations to preserve only N=1 space-time supersynimetry should be 3, 4,6,7,8 and 12.3)The simplest orbifold among them is the Z3 orbifold,2) whose. models have been studied in detail and classified into five types (including a model with the unbroken E8 X E8 gauge group). But these five models are far from realistic. That requires so·me mechanism to lead to real world theory, e.g., the Wilson line mechanism.It has been shown in recent papers 4 ),5) that the Z4, Z6 and Z7 orbifold models are obtained through the same construction as one of Z3 orbifold models and that the Z4, Z6 and Z7 orbifold models have more diverse and smaller gauge groups than ones of Z3 orbifold. The other ZN orbifold models can be obtaiqed in the same way as the above one and it can be expected that they also have more variant, smaller and more realistic gauge groups. Here, we study all gauge groups that can be got from ZN orbifolds.In § 2 we review the construction of ZN orbifold models and the division of the six-dimensional space which preserve N=1 space-time supersymmetry. In § 3, we discuss breakings of an E8 group and classifications of ZN orbifold models. Conclusions and discussion are given in the last section.
We investigate a dynamical mechanism to generate fermion mass in the Randall-Sundrum background. We consider four-fermion interaction models where the fermion field propagates in an extra-dimension, i.e. the bulk four-fermion interaction model. It is assumed that two types of fermions with opposite parity exist in the bulk. We show that electroweak-scale mass is dynamically generated for a specific fermion anti-fermion condensation, even if all the scale parameters in the Lagrangian are set to the Planck scale.
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