Before LEP experiments have excluded simple technicolor models, I have
studied extended technicolor models as a scenario of the fermion masses
generation. The values of S and T parameters, which describe the radiative
corrections to the propagators of weak bosons, has been strongly constrained
by LEP experiments. The value of S parameter must be very small in comparison
with the values predicted by simple technicolor models. I constructed with
T.Yanagida a technicolor model which naturally gives small values of S and T
parameters. We proceeded further to explain about 3-sigma deviation of the
experimental value of R_b from the standard model prediction within this model.
Although the model works very well, the experimental value of R_b was changed
and the deviation had disappeared.
Since I thought Grand Unified Theories could not give an explanation for fermion mass
hierarchy (they in general include many parameters if we consider full Higgs sector),
I changed my direction to the composite models in which the Yukawa couplings for fermion
masses should be dynamically generated. The dynamics of the supersymmetric gauge
theories is a good candidate of the underlying dynamics of the composite model
because of the remaining chiral symmetry for having massless fermion bound states.
I constructed with N.Okada a model which includes necessary breaking of supersymmetry
and electroweak symmetry. It is a toy model which includes only third generation, and
its basic structure is the same of the model by A.E.Nelson and M.J.Strassler. I proceeded
further to include other two generations. Although I have constructed a concrete realistic
model, it is very complicated.
Since I thought the construction of concrete models by just combining known
mechanisms could not solve the problem, I changed my direction to study some
important parts of the model. The topics that I chose was the dynamics of the
supersymmetry breaking. It is very artificial to introduce an independent
sector (gauge symmetry and matter) just for supersymmetry breaking. Almost
all the proposed models had this structure. I constructed with N.Maru and
N.Okada several concrete models of dynamical supersymmetry braking in which
the gauged U(1)_R symmetry in supergravity theories is utilized. Because of
the symmetry of supergravity theory, the U(1)_R gauge field must have
Fayet-Iliopoulos term which can trigger the supersymmetry breaking. This fact
had already been known, but there was no concrete model, since the cancellation
of anomalies of gauge U(1)_R symmetry was considered to be very difficult.
Although our mechanism was not the ideal one, because it includes an additional
gauge group for supersymmetry breaking, the supersymmetry breaking due to the
interplay between supergravity and gauge dynamics was a new mechanism.
There is a possibility that the supersymmetry is spontaneously broken by the
fermion condensation in String Theory. A concrete example of such system
has already given in four-dimensional supergravity theories. In the system the
gravitino condensation by some non-trivial space-time backgrounds breaks
supersymmetry spontaneously. I made an effort to clarify whether such phenomena
is possible or not in String Theory, which may be a consistent theory of
quantum gravity. I found that the tension of D3-brane in type IIB string theory
in flat space-time is different from that in the flat space-time limit
of the fivebrane background. This suggests the existence of some condensations
due the the topological effect of the fivebrane background, since it can be
shown that the value of tension is modified only by such condensate. It is
probable that some composite operators of fermions condensates. It is not clear
whether such condensations have some relation to the half supersymmetry
breaking by fivebrane backgrounds. I also studied the explicit form of
the fermion zero-modes in fivebrane backgrounds in low-energy effective
theories of some string models.
There are vary few researches on the fermion dynamics in String Theory using
the technique of the world-sheet conformal field theory. I have calculated the
propagators of fermion fields (gravitino, dilatino and gaugino) in some string
models, and made an attempt to get some information of the fermion
condensation. I have succeeded to evaluate the gaugino pair condensation in the
fivebrane background of heterotic string theory. The value is proportional to
the value of the B-field field strength in non-trivial four-dimensional space
in the fivebrane background. Although it is possible that the condensation
gives some contribution to the central charge in the ten-dimensional
supersymmetry algebra (the central charge is required for the half
supersymmetry breaking by the fivebrane background), the meaning and role of
the condensation is still to be clarified.
After these formal works on String Theory, I came back to the flavor problem of
quarks and leptons. I recognized that so-called intersecting D-brane model
can open new world in the phenomenological model building in String Theory.
The gauge symmetries are realized through the introduction of D-branes and
the chiral fields are realized on the D-brane intersecting points in extra
six dimensional space of type IIA or IIB string theory. Especially, the way
to realize the gauge symmetry is very different from that in heterotic string
models, and even the strong coupling gauge interactions in the visible sector
can be realized. In the model buildings (without flux), I found a problem that
we need too many D-branes to satisfy consistency conditions (Ramond-Ramond
tadpole cancellation conditions as well as supersymmetry conditions). It means
that we are forced to introduce some extra gauge symmetries in addition to
the one in the standard model. It also means that we are forced to have rather
many exotic particles which do not exist in nature. I proposed that these
extra gauge interactions can be identified to the confining forces of preons
which are the constituents of quarks and leptons. Namely, I proposed to
introduce compositeness of quarks and leptons (and Higgs doublet fields).
As a bonus we can have non-trivial Yukawa couplings among fermions (quark and
leptons) and Higgs doublet fields, which is difficult to obtain in usual models.
The "non-trivial Yukawa coupling" means that it can realize rather realistic
hierarchical quark masses and their flavor mixings, which is difficult to
be realized in usual models with elementary quarks and leptons (and Higgs
doublet). The point is that the origin of the generation in composite models
is different from that in the usual models. The multiple intersection of
D-branes is the origin of the generation in usual models, while the D-brane
splitting as well as the multiple intersection of D-branes are the origin
of generation in composite models.
In the typical models using D-branes, like intersecting D-brane models, for example, supersymmetry is utilized to obtain stable configurations of D-branes. Therefore, their realistic low-energy effective theory is likely to be the minimal supersymmetric standard model. In the minimal supersymmetric standard model a certain special pattern of supersymmetry breaking is necessary for the electroweak symmetry breaking. Since the mechanism of supersymmetry breaking is difficult to be explicitly incorporated in string models from the beginning, this means that the realization of the electroweak symmetry breaking is a challenging problem in typical string models using intersecting D-branes. The system of D-branes at orbifold singularities gives a possible framework towards obtaining stable models without supersymmetry. The standard model may be realized on the D-branes at an orbifold singularity in compact extra six-dimensional space. In case that the orbifold singularity breaks supersymmetry, we can obtain a model without supersymmetry. In this class of models the electroweak symmetry breaking can be triggered by the vacuum expectation value of elementary Higgs doublet fields through the non-trivial radiative corrections due to no supersymmetry. This is the radiative electroweak symmetry breaking in which the breaking is necessary and inevitable without naturalness problem. The scale of the electroweak symmetry breaking is determined by the scale of the string tension, or the strang scale, which should be at around TeV scale. I have proposed this scenario by constructing a concrete model, though some theoretical problems remain (the NS-NS tadpole problem, which is expected to be solved by "tadpole resummations", and the closed string tachyon problem, which is expected to be solved by constructing models based on Sagnotti's type 0'B string model). If this scenario was true, some string phenomena could be observed at the LHC.
In case that the string scale is of the order of TeV scale, a peak in the dijet invariant mass distribution by string resonances should be observed at the LHC. Within the situation that some other possible physics beyond the standard model also predict such peaks, I have pointed out some strategy to clarify whether the peak is string origin or not. The key aspect is that several string resonances of the same mass with different spins should simultaneously contribute to a peak, and investigating the angular distribution of dijets from the resonance should solve the problem. I have carried out extensive Monte Carlo simulations of LHC experiments with M.Hashi, and future discovery potential of the resonance and the possibility of the angular analysis have been clarified.
The system of D-brane without supersymmetry generally has NS-NS tadpole problem, which indicates the assuming background space-time is not the solution of String Theory. The practical problem is that the open-string one-loop quantum corrections, which should be focused with much interest in the system without supersymmetry, diverge by the infrared singularity in the tree-level exchange of massless closed string states with tadpole couplings with D-branes. The procedure of Fischler and Susskind is famous to solve this problem, but unfortunately it is very difficult to do it in practice. On the other hand, the procedure of "tadpole resummations" which was proposed by Dudas, Nicolosi, Pradisi and Sagnotti, seems more practical way of doing. I have shown that it is really possible to do it in String Theory, and obtained a further evidence of Sen's conjecture, namely, the tachyon condensation on D25-brane in bosonic string theory. I have also developed the formulation to calculate the one-loop corrections to the masses of scalar field towards clarifying the possibility of radiative gauge symmetry breaking in String Theory.
LHC experiments discovered Higgs particle in the standard model without any signatures beyond the standard model. Which indicates that the energy scale of the physics beyond the standard model is much higher than expected. In case that the string scale is very large, it is impossible to observe the effect of String Theory in collider experiments. One may hope that such a high energy physics acts a role in very early universe, especially in the inflation of the universe. In a class of string model with "brane supersymmetry breaking" the scalar field which follows exponential potential is predicted. During the classical evolution of the universe from Big-Bang singularity, since the exponential potential is too steep, the scalar field is forced to climb the exponential potential and turn its motion to descend the potential. If we identify the scalar field as a inflaton, with some corrections to the potential for late-time inflation, it is possible that such a motion of scalar field leaves an imprint in the power spectrum of perturbations of the cosmic microwave background. I have examined with A.Sagnotti the possible deformations of the power spectrum by this "climbing scalar" and compare them with the observed power spectrum by WMAP and PLANCK collaborations.
The imprint of the "climbing scalar" in the cosmic microwave background typically appears as a systematic lack of powers of large scale perturbations. Such a distorsion of the power spectrum can be phenomenologically modelled by introducing one additional parameter to the standard model of cosmology: the LambdaCDM model. With some members of the PLANCK collaboration, A.Gruppuso, M.Lattanzi, N.Mandolesi and P.Natoli and also with A.Sagnotti I have obtained a precise fit of the parameter with the observed power spectrum by PLANCK collaboration. Amazingly, the additional parameter makes the fit of the theory to the observation better, which means that a systematic suppression of large scale perturbations exists. Such a suppression becomes clearer for larger galactic masks. At present we may be looking the beginning of the inflation through the larger scale perturbations of the cosmic microwave background.
The behavior of D-branes in the situation without supersymmetry has not yet been fully clarified. This should be a key subject to understand spontaneous gauge symmetry breaking and moduli stabilization of extra six-dimensional compact space in superstring theory, which are necessary to connect String Theory to the particle physics. I have tried with S.Kobayashi to understand spontaneous breaking of gauge symmetry with reducing its rank through the parallel separation of D-branes in such way that they are identified by discrete symmetry of orbifold. Such a configuration is possible under the balance of forces between D-branes in the situtation without supersymmetry. Such a balance of forces could happen in a more dynamical way like a binary stars. I have studied the system of revolving D-branes both from the phenomenological and dynamical point of view with S.Iso, T.Suyama and H.Ohta.
The nature of Dark Energy, which realizes recent accelerating expansion of the universe, is also the physics beyond the standard model. Since the polarizations of large scale perturbations of the cosmic microwave background are produced rather recently, it is probable that the polarization power spectra of large scale perturbations carry some information of Dark Energy. Indeed recent history of cosmic expansion affects the power spectra, since the polarizations are produced through Thomson scattering off free electrons whose density depends on the history. The expansion history appears in measurements of the values of Hubble parameters at various values of redshift. Now there are two different results depending on the methods to measure the distance: the standard distance ladder and the inverse distance ladder. I have found that the case of the standard distance ladder, which gives unexpectedly larger value of Hubble parameter than that has been obtained by PLANCK collaboration, gives an enhancement of the polarization power spectra of large scale perturbations.