Z12−I Orbifold Compactification toward SUSY Standard Model

The standard model (SM) with 45(+3) chiral fields is really remarkable. The big question in particle physics is, “How does this SM arise?” In late 1980s, there were attempts for standard-like models (which has three families with the gauge group SU(3)×SU(2)×U(1)) 1 from the orbifold compactification of heterotic string. Recent attempts have been more ambitious but it is fair to say that a model free of any phenomenological problems has not appeared yet even though partially attractive ones have been proposed in trinification, Pati-Salam, or just SM2. So, searches for good supersymmetric (SUSY) standard models (SSM) are going on now vigorously. Even some string models are suggested as roots for explaining the PVLAS data 3. In this talk, I follow the compactification route through orbifolds. Orbifolds are manifolds modded by discrete actions. A nice feature of the orbifold compactification is that it is basically a geometric one. For an SSM, we may obtain it either directly from compactification or through an intermediate step of SUSY GUT. In Z12−I , we have constructed both kinds 4,5, and here we focus on the direct construction. In the orbifold construction, there has been the adjoint difficulty that at the KacMoody level k = 1 there does not appear an adjoint matter representation. Thus, GUTs SU(5), SO(10), and E6 are not good candidates toward SSMs simply because the Higgs mechanism for breaking the GUT group is not present. This prefers GUTs with factor groups such as SU(3), SU(4)×SU(2)×SU(2) and SU(5)×U(1). The trinification SU(3) is possible only in Z3 which is nice toward achieving 6 sin θW = 3 8 . In addition to the sin θW problem, there are several problems to be