SO ( 10 ) GUTs in Higher Dimensions

We discuss supersymmetic SO(10) unified theories constructed in 6 dimensions. The breaking of SO(10) group is achieved by the orbifold compactification. In 4 dimensions we obtain a N = 1 supersymmetric standard model which gauge group is enlarged by an additional U(1) symmetry. This unbroken gauge group is obtained as intersection of the Pati-Salam and the Georgi-Glashow subgroups of SO(10). The doublet-triplet splitting in Higgs multiplet arises as in SU(5) models in 5 dimensions. ∗This talk is based on the works with W. Buchmüller and L. Covi [1]. 5: Grand Unification 1265 The supersymmetric grand unified theory (GUT) is an attractive physics beyond the standard model. The simplest GUT to unify electroweak and strong interactions is based on the SU(5) gauge group [2]. With the present experimental evidence for neutrino masses and mixings the larger gauge group SO(10) [3] appears particularly attractive, since it unifies one family of quarks and leptons, including the right-handed neutrino, in a single irreducible representation. However, we have to overcome several issues in the construction of a successful GUT model. The breaking of GUT gauge groups is in general rather involved and requires often large Higgs representations. In particular, the serious problem is how to achieve the mass splitting between the weak doublet and the color triplet Higgs fields. An attractive solution to these issues has been suggested by Kawamura [4] in the case of SU(5) GUT in 5 dimensions (5d). Compactification on the orbifold S/(Z2 × Z ′ 2) offers a simple and elegant explanation of the SU(5) breaking into the standard model gauge group GSM= SU(3)×SU(2)×U(1) as well as the wanted doublet-triplet splitting. Various aspects of such SU(5) GUTs in 5d have been extensively studied [5]. In this talk we would like to discuss the breaking of the SO(10) GUT group by the orbifold compactification. In contrast to the SU(5) case the SO(10) breaking is not straightforward. In fact, an ideal breaking pattern of SO(10) into the standard gauge group GSM cannot be obtained by the orbifold boundary conditions (of inner automorphism). This is because the orbifold breaking does not reduce the rank of the gauge group and also because GSM is not a symmetric subgroup of SO(10). 1 However, it is remarkable that the extended standard model group, GSM ′=GSM×U(1), is the maximal common subgroup of two symmetric subgroups of SO(10), say GPS = SU(4)× SU(2) × SU(2) [7] and GGG = SU(5) × U(1) (cf. Figure 1). This suggests that the SO(10) breaking into GSM ′ (rather than GSM) can be realized by starting from the six dimensional theory and by orbifolding to the two different subgroups in the two orthogonal compact dimensions. This is the reason why SO(10) GUTs are constructed in 6d [1, 9]. Let us consider a SO(10) Yang-Mills theory in 6d with N = 1 supersymmetry (SUSY). The gauge multiplet consists of gauge fields AM (M = 0, 1, 2, 3, 5, 6) and two gauginos λ1 and λ2. In the usual 4d superspace, they correspond to one vector superfield V = (Aμ, λ1) and one chiral superfield Σ = (A5,6, λ2). Here μ = 0, 1, 2, 3, V = V T a and Σ = ΣT a with SO(10) generators T . The action for the gauge multiplet is given by [10] S6d = ∫ dx { Tr [ ∫ dθ 1 4k W Wα + h.c. ] For a general discussion of the orbifold breaking, see, e.g., Ref. [6]. SO(10) breakings into GPS and GGG can be done similar to the SU(5) model in 5d. See, e.g., Ref. [8]. 1266 Parallel Sessions