Mitsuo J. Hayashi

Radiative breaking of SU(2)R×U(1)B−L gauge symmetry induced by broken N = 1 supergravity in a left-right symmetric model

Abstract The radiative breaking of SU(2) R ×U(1) B−L gauge symmetry induced by broken N = 1 supergravity is investigated in a left-right symmetric GUT with SU(3) C ×SU(2) L ×SU(2) R ×U(1) B−L as the intermediate symmetry. If the trilinear scalar coupling parameter A =3 at a GUT scale M X ∼10 14−15 GeV, SU(2) R ×U(1) B−L can indeed be broken almost simultaneously with the SUSY breaking at M W R ∼10 4±1 GeV for sin 2 θ w ( M W L )≈0.19−0.20. The scalar partner of right-handed τ -neutrino triggers the breaking and its vacuum expectation value inevitably violates R parity giving rise to the mixing among neutral fermions including “inos”, which suggests a “generalized see-saw mechanism” for light neutrino mass generation and predicts single-sparticle production.

Dilatonic Inflation and SUSY Breaking in String-inspired Supergravity

The theory of inflation will be investigated as well as supersymmetry breaking in the context of supergravity, incorporating the target-space duality and the nonperturbative gaugino condensation in the hidden sector. We found an inflationary trajectory of a dilaton field and a condensate field which breaks supersymmetry at once. The model satisfies the slow-roll condition which solves the η-problem. When the particle rolls down along the minimized trajectory of the potential V(S,Y) at a duality invariant point of T=1, we can obtain the e-fold value ~57. And then the cosmological parameters obtained from our model well match the recent WMAP data combined with other experiments. This observation suggests one to consider the string-inspired supergravity as a fundamental theory of the evolution of the universe as well as the particle theory.

THE COSMIC STRINGS GENERATED FROM THE TORSION

The cosmic strings can be described naturally by torsion formalism which has a direct analogy with dislocations in three-dimensional crystalline solid. We have obtained an exact solution in a four-dimensional model on M2×T2 and may be expected to describe a space-time structure of our universe. The relation between the mass per unit length and the deficit angle are different from that of the Einstein theory, but can be made consistent since our model could reproduce its prediction. We could also obtain the maximum value of the mass per unit length µ~10−6(~1022g/cm) by fine tuning of a parameter, which is consistent with the recent observations.

ANGULAR POWER SPECTRUM IN MODULAR INVARIANT INFLATION MODEL

We propose a scalar potential of inflation, motivated by modular invariant supergravity, and compute the angular power spectra of the adiabatic density perturbations that result from this model. The potential consists of three scalar fields, S, Y and T, together with two free parameters. By fitting the parameters to cosmological data at the fixed point T = 1, we find that the potential behaves like the single-field potential of S, which slowly rolls down along the minimized trajectory in Y. We further show that the inflation predictions corresponding to this potential provide a good fit to the recent three-year WMAP data, e.g. the spectral index ns = 0.951. The TT and TE angular power spectra obtained from our model almost completely coincide with the corresponding results obtained from the ΛCDM model. We conclude that our model is considered to be an adequate theory of inflation that explains the present data, although the theoretical basis of this model should be further explicated.

Three-generation model of the heterotic string compactified on the six-torus

Abstract The number of generations is computed in the E 8 × E 8 heterotic string compactified on a six-torus T 6 in the field theory limit. It is given by the imdex of the Dirac operator for a principal fiber bundle on T 6 with the structure group F ⊂ E 8 . When F = SU (N) and twisted boundary conditions are imposed, the case N = 4 has the possibility to realize a three-generation model with the gauge group SO(10), while the cases N = 3 and 5 (corresponding respectively to the gauge group E 6 and SU(5)) are excluded because of the fractionality of the index.

DILATONIC INFLATION AND SUSY BREAKING IN MODULAR-INVARIANT SUPERGRAVITY

The theory of inflation will be investigated as well as supersymmetry breaking in the context of supergravity, incorporating the target-space duality and the non-perturbative gaugino condensation in the hidden sector. The inflation and supersymmetry breaking occur at once by the interplay between the dilaton field as inflaton and the condensate gauge-singlet field. The model satisfies the slow-roll condition which solves the eta-problem. When the particle rolls down along the minimized trajectry of the potential V(S,Y) at a duality invariant fixed point T=1, we can obtain the e-fold value \sim 57. And then the cosmological parameters obtained from our model well match with the recent WMAP data combined with other experiments. This observation is suggesting to consider the string-inspired supergravity as the fundamental of the theory of the evolution of the universe as well as the particle theory.

SPIN-3/2 FERMIONS IN TWISTOR FORMALISM

Consistency conditions for the local existence of massless spin-3/2 fields have been explored to find the facts that the field equations for massless helicity-3/2 particles are consistent if the space–time is Ricci-flat, and that in Minkowski space–time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity-3/2 fields, we show in flat space–time that the charges of spin-3/2 fields, defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space–time that the (anti-)self-duality of the space–time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space–time to that with torsion (Einstein–Cartan theory), and investigate the consistency of existence of spin-3/2 fields in this theory. A simple solution to this consistency problem is found: The space–time has to be conformally (anti-)self-dual, left-(or right-) torsion-free. The integrability condition on α-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed torsion.

EXACT COSMIC STRING SOLUTIONS BASED ON THE CONTINUUM THEORY OF DISLOCATIONS

The effective action from the string compactification is studied on the manifolds with absolute parallelism. The cosmic strings can be described naturally by torsion formalism which has a direct analogy with dislocations in three-dimensional crystalline solids. We have found a stringy solution in a six-dimensional model on M4 × T2 which is compatible with that of Greene et al. and a cylindrically symmetric exact solution is obtained, which are different from the exact cosmic string solutions of the Einstein theory ever proposed. We have also obtained an exact solution in a four-dimensional model on M2 × T2 which can be considered as an example of the compactification on the noncompact manifold and may be expected to describe a space–time structure of our universe. The relation between the mass per unit length and the deficit angle is different from but can be consistent with that of the Einstein theory, since our solution could reproduce its prediction with a condition. We could also obtain the maximum value of the mass per unit length μ ~ 10−6 (~ 1022g/cm) by fine-tuning a parameter, which is consistent with recent observations. We have discussed the cosmic strings with the deficit angle larger than 2π.

What is the Role of Torsion in the Universe

The effective action from the heterotic string compactification is studied on the manifolds with absolute parallelism. The cosmic string solutions resulting from the effective action are discussed in analogy with the dislocations in three-dimensional crystalline solid. The cosmic string density is concluded to be given by the torsion tensor of space-time, which gives rise to a compactification at least in one-dimensional direction in space-time. It is shown also the contorsion tensor defines the deficit angle. We have found a stringy solution in a sixdimensional model on M 4 × T 2 which is compatible with that of Greene et al. and a cylindrically symmetric exact solution is obtained, which are different from the exact cosmic string solutions of the Einstein theory ever proposed

ARE THE COSMIC STRINGS SEEN AS THE DISLOCATIONS

The effective action from the heterotic string compactification is studied on the manifolds with absolute parallelism. The cosmic string solutions resulting from the effective action are discussed in analogy with the dislocations in 3-dimensional crystalline solid. The cosmic string density is concluded to be given by the torsion tensor of space-time, which gives rise to a compactification at least in 1-dimensional direction in space-time. It is also shown that the contorsion tensor defines the deficit angle. We have found a stringy solution in a 6-dimensional model on M4 × T2 which coincides with that of Greene et al.,5 but the string energy density depends only on torsion, therefore independent of the space-time metric.