Katsuji Yamamoto

Peccei-Quinn symmetry breaking by radiative corrections in supergravity

Abstract We investigate the Peccei-Quinn symmetry U(1)PQ in supersymmetric theories coupled to N = 1 supergravity. U(1)PQ is identified with a usual global symmetry of the superpotential, rather than an R-symmetry which is explicitly broken by the soft supersymmetry breakings induced by supergravity. The scale of U(1)PO breaking is found to be M PQ ∼M Planck × exp ( −4π λ 2 )∼10 8−12 GeV , as determined by the logarithmic evolution of soft supersymmetry breakings.

Saving the Axions in Superstring Models

In the effective four-dimensional supersymmetric theories derived from the superstring theories, we investigate a possible way to evade the cosmological bound ƒa≲1012GeV on the axion decay constant. A significant amount of entropy could be produced by the out-of-equilibrium decay of the Higgs field which is responsible for the breaking of the extra gauge symmetry at an intermediate mass scale MI. The appearance of such a Higgs fiield is a general feature of the superstring models. We find that if the gravitino mass m32∼1−102 GeV and MI∼107−1010 GeV, the axions are diluted efficiently by the entropy production, and ƒa∼O(1016 GeV) will still be acceptable.

Effects of grand unification interactions on weak symmetry breaking in supergravity theories

Abstract Possible effects of grand unification interactions on SU(2) × U(1) breaking are investigated by explicitly considering a supersymmetric SU(5) model coupled to N = 1 supergravity. Some remarkable features concerning the effects of renormalization on the effective soft supersymmetry breaking terms of SU(5) in the GUT region MP − MG are clarified, which are relevant for determining the SU(3) × SU(2) × U(1) theory below MG. In particular, the (mass)2 of the Higgs doublets, g H m g 2 and g H m g 2 , might become significantly small at M G (g H ⋍ g H ≈ 0.1) through the effect of SU(5) couplings such as H o E H . Then, gH can rather easily become negative below MG, so as to realize SU(2) × U(1) breaking naturally even for the “diet” top quark case (mt ≈ 40 GeV). On the other hand, if g H ⋍ g H ⋍ 1 at M G by neglecting the grand unification interactions, some careful tuning of μ32/mg2 is required with an accuracy ⪅10−2 to achieve SU(2) × U(1) breaking with “diet” top quark, though a mass term μ 3 2 ( H H ) may be present.

Grand Unification Symmetry Breaking by Radiative Corrections in Supergravity

Abstract We investigate the breaking of grand unification symmetry by radiative corrections in a class of supersymmetric theories coupled to N = 1 supergravity. Such theories have a continuum of supersymmetric minima in the absence of supergravity couplings. The potential minimum is actually generated in the desired region, M G = M P /10 1–4 , due to the logarithmic evolution of a Higgs mass term of soft supersymmetry breaking induced by the supergravity coupling.

Spontaneous compactification and chiral fermions

Abstract The question is addressed of which chiral fermions survive in spontaneously compactified solutions of the generalized Einstein-Yang-Mills field equations for higher even space-time dimensions. First, we study the allowed fermion representations of SU( N ) which have no gauge or gravitational chiral anomalies in arbitrary even dimension and show how to find all such representations for the case of totally antisymmetric SU( N ) tensors. Second, we look explicitly at monopole-induced spontaneous compactification in six dimensions; here, interesting chiral fermions in four dimensions do not occur easily but instead require highly artificial assignments of quantum numbers under the U(1) gauge group associated with the monopole. Finally, we consider instanton-induced spontaneous compactification in eight dimensions; for this case, we may readily obtain acceptable chiral fermions in four dimensions, including Georgis three-family SU(11) model.

Results on stability of instanton-induced compactification in eight dimensions

Abstract In an eight-dimensional Einstein-Yang-Mills system with the Yang-Mills field in a one-instanton configuration on an internal S 4 with a vacuum invariant under P 4 (Poincare) × SO(5) we demonstrate classical stability for Yang-Mills gauge group SU( N ) or SO( N ) for any N .

Finite Temperature Behavior of Gauge Hierarchy Models With Quantum Mechanical Resuscitation

Abstract We investigate the finite temperature behavior of Dimopoulos and Georgis hierarchy model where the grand unification scale M G is naturally generated by the quantum corrections. Owing to the particular form, M 2 π 2 ( e 2 ln π − 1), of the scalar potential, the first order GUT phase transition takes place at the critical temperature T c ∼ 10 9−12 GeV much lower than M G . If M G should be of O( M P ) (Planck mass), the universe may undergo an inflationary stage to expand enough. Baryon number asymmetry might be produced by the decay of colored scalars with a mass of 10 10−12 GeV.

Weak anomaly cancellation in even dimensions

Abstract The gauge anomaly for dimension d=2n⩾6 contains several irreducible components. The leading component must be cancelled, but the nonleading parts may be either cancelled or compensated by introducing new fields. The latter mechanism is illustrated by a few examples.

SO(18) family unification in eight-dimensional space-time

Abstract We investigate an SO(18) gauge theory in an instanton-induced compactified manifold M 4 × S 4 . The instanton is embedded in a diagonal subgroup SU(2) 2+3 of SO(18) ⊃ SO(10) × SU(2) 1 × SU(2) 2 × SU(2) 3 × SU(2) 4 . The effective gauge theory in Minkowski space M 4 is described by SO(10) × SU(2) 1 × Su(2) 4 × SU(5), and a set of chiral fermions are obtained in the harmonic expansion of one complex SO(18) spinor representation of Weyl fermions in eight dimensions. These fermions contain four ordinary families and four mirror families. Some crucial roles of the isometry SO(5) are clarified concerning the family problems and the low-energy phenomenology.

Left-right gauge symmetry breaking by radiative corrections in supergravity☆

Abstract A supersymmetric SU(2) L × SU(2) R × U (1) B − L gauge theory coupled to N = 1 supergravity is investigated. The scale of left-right gauge symmetry breaking is determined as M R ∼ M P e −1/ α by radiative corrections through the logarithmic evolution of soft supersymmetry breakings. SU(2) L × SU(2) R × U (1) B − L may be embedded in SO(10) grand unification. Cosmological implications intrinsic to the present model are also discussed, which may give a constraint M R ∼ 10 9−12 GeV .