**
RESEARCH INTERESTS**

**Cosmology Supersymmetry and Supergravity Strings and Superstrings
Branes and M-Theory Conformal Field theory
Non-linear Sigma-models**

*Motivation:*

The quest for an ultimate unified theory of all fundamental physical
interactions is the most prominent and important problem of modern theoretical
high-energy physics. The ultimate (i.e. most fundamental) physical theory
must go beyond the so-called **Standard Model** of elementary particles,
it must include **quantum gravity**, and it should explain the **origin
of our Universe.** The practical significance of the unified theory goes
far beyond the high-energy physics, since it may provide the keys to many
unsolved actual problems in astrophysics and condensed matter, such as
physics **inside** black-holes, **early** Universe, and **strong**
coupling. *There is nothing more practical than a good theory!*

The superstring theory is the leading candidate for quantum gravity
and physics beyond the Standard Model. However, a perturbative vacuum
in any superstring model is highly degenerate, whereas the effective physics
at low energies heavily depends upon the choice of vacuum. To make contact
with the Standard Model, one has to investigate **non-perturbative**
superstring vacua.

The recently proposed **M-Theory** unifies all known ten-dimensional
superstring theories, as well as the eleven-dimensional supergravity. M-Theory
also has extra symmetries (called **dualities**) that relate weak
and strong coupling regimes. The key ingredients of M-Theory are the extended
objects called **BPS branes** that are essentially non-perturbative
(solitonic). Amongst the solitonic branes there are the so-called **D-branes
**where open superstrings can have their ends. Since the fundamental degrees
of freedom in M-Theory are unknown, this theory cannot be applied from the
first principles yet. Nevertheless, in the **semi-classical** approach,
some non-perturbative corrections can be captured by the BPS branes.

*Some Research Projects:*

[1] Our most recent research interests are related to **supergravity**
and its applications to **Cosmology**. We are interested in various viable
realizations of cosmological **inflation** in the early Universe, as well
as that of **Dark Energy** in the present Universe, in the context of
supergravity, and their relation to Particles Physics, and **supersymmetry
breaking**, in particular.

[2] Some instanton corrections to the superstring low-energy effective
action arise due to the (Euclidean) BPS branes **wrapped** about certain
surfaces (cycles) in the compactified space (usually, a Calabi-Yau threefold).
A derivation of the corresponding low-energy effective supergravity action
in four or five spacetime dimensions is one of the actual problems in M-Theory.
Our approach to this problem is based on the use of **integrable systems**
and ** complex ** differential geometry.

[3] Another proposal deals with part of M-theory that is supposed to
explain how Maxwell **electrodymanics** is going to be generalized in
M-theory. There are strong arguments coming from M-theory that the correct
generalization of the Maxwell electrodynamics is given by some kind of
the (non-linear) abelian **Born-Infeld** theory. We would like to
generalize those arguments to the case of several coinciding branes where some
**non-abelian** Born-Infeld-type gauge theory emerges, whose leading term
is given by the standard Yang-Mills action. The Born-Infeld theory gives rise
to the famous taming of Coulomb self-energy of a point-like electric charge.
It also shares (in four dimensions) with the Maxwell theory
**electric-magnetic self-duality **as well as physical propagation
(no shock waves). In fact, the Born-Infeld I theory has even more magical
properties, such as the built-in upper bound for the electro-magnetic
field-strength and the existence of exact soliton-like solutions of finite
total energy. In addition, when a **constant** Kalb-Ramond background
B-field is turned on, the Born-Infeld theory in some limit becomes equivalent
to a **non-commutative** U(1) gauge field theory in flat spacetime via the
so-called **Seiberg-Witten map **. The supersymmetric extensions of the
abelian Born-Infeld action can be identified with the **Goldstone-Maxwell
**actions associated with **partial **(1/2) spontaneous **supersymmetry
breaking**, whose Goldstone fields belong to a Maxwell (vector)
supermultiplet with respect to unbroken supersymmetry. The supersymmetric
Born-Infeld actions in various dimensions also represent the **worldvolume**
low-energy effective actions of D-branes. We want to determine the interaction
(couplings) of the D-brane worldvolume fields to the bulk fields.

*Message to the Students of all Levels:*

We are looking for ambitious students who would like to join our group and
actively participate in our research projects. The eariler one begins is the
better. We particularly encourage students with independent thinking and
strong interest to applied mathematics in theoretical physics.

*Our Special Message to Foreign Students:*

Tokyo Metropolitan University and our group welcome applications from qualified foreign (non-japanese) students. Formal applications are accepted in January each year for the Doctor (PhD) Course, and in September and January each year for the Master (MS) Course. Written entrance exams and interviews for the MS course are held in September and February each year, interviews for the PhD Program are held in January. Students in the MS program are required to carry out a course of their study, supervised by a TMU staff member, culminating in a Master Thesis which may contain original research results. Students in the PhD Program are required to carry out a research project supervised by a TMU staff member, and to write a Doctoral Thesis which must contain original and substantial new research results.

The entrance examinations and/or interviews, as well as the entire course of study, may be carried out in English, although most of lectures and seminars are held in Japanese. Hence, some knowledge of Japanese language will be helpful for communication with other students and staff, as well as for daily life. Japanese language courses, both formal and informal, are available for foreign students. Prospective students are strongly advised to contact a TMU staff member for further advice.

Japanese Government Scholarships are the principal source of financial support for
foreign students. Information concerning the Scholarships is available from the Japanese
Embassies and their web-sites. In general, such Scholarships permit the holder to enter
Tokyo Metropolitan University as a `research student' and then prepare for the exams to enter
the Graduate School for the chosen Course.