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String theory provides a precise mathematical structure
to address questions in low energy gravity, black hole
physics, and realizes a fruitful and promising
tool for construction of phenomenologically realistic
models of elementary particle physics.
It is a leading candidate for the consistent unification
of gravitation and quantum mechanics.
Much of the progress in string theory is attributed
to understanding of static (time-independent) backgrounds, while
deep cosmological foundations like the origin of time,
the physics of space-like singularities, and the cosmological
constant problem until recently appeared to be out of its
grasp. Recently, important progress
has been made toward formulating string theory in a
cosmological setting. There is a hope that these new
developments will help us understand the
Universe we are living in.
Analysis of the fluctuations of the
Cosmic Microwave Background, when combined with the
results of Type Ia supernovae observations,
convincingly demonstrate the acceleration of
our Universe.The simplest cosmological model to account for
this result involves background space-times
with a positive cosmological constant.
However, corresponding de-Sitter space-time
(and thus the presence of a genuine
nonzero vacuum energy) present conceptual problems
for the formulation of the string theory, when defined as an S-matrix theory.
The problem is related to the existence
of event horizon in de-Sitter space-time, which implies that it is not
possible to construct a conventional S-matrix:
a local observer inside his horizon is not able to
isolate particles to be scattered. We proposed an
alternative to a conventional S-matrix definition for string
theory in accelerating universe.
The basic idea is to exploit the correspondence between string
theory and gauge theory, and rather when defining string theory
as an S-matrix theory, realize it as a Quantum Field Theory
in background de-Sitter space-time.
The proposal provides a confirmation to the physical intuition
that spontaneously broken symmetries of gauge theories
are restored in accelerating universe, provided the
Hubble scale is large enough.
It can thus be used as an analytical tool to study these
Much of the details
of this "deformed" Maldacena correspondence remains to be uncovered.
One of the fundamental problems in cosmology is the origin of time and the orientability of the time arrow at the macroscopic level. Recently, Sen proposed to identify time in quantum cosmology with a scalar field (tachyon) representing a decay of an unstable D-brane (or brane anti-brane pair). Additionally, the non-equilibrium decay process naturally defines the direction of the entropy growth, and thus the macroscopic arrow of time. As the tachyon rolls down the potential, one is left with an interesting state of matter --- the "tachyon matter" which has finite energy density but the exponentially vanishing pressure. Tachyon matter has attracted considerable cosmological interest. We proposed and studied an effective field theoretical model describing a decaying tachyon on an unstable D-brane in string theory. Asymptotically, the tachyon field decouples from the supergravity modes, and the far future geometry approaches that of the space-like branes, S-branes. We proved that inclusion of the tachyon destabilizes the horizon of an S-brane to a genuine space-like curvature singularity. Such a singularity is expected on physical grounds in the supergravity approximation, where an S-brane is identified as a source of a space-like topological defect. An important open problem is the mechanism for the resolution of the space-like singularity of the unstable D-brane decay (or S-brane). I am currently working on this issue. It is likely that the observed singularity is the rudiment of the supergravity approximation. It is known that in the framework of the Boundary String Field Theory, which motivated our effective model, the rolling tachyon coupling to massive closed string modes becomes strong at string-scale times. Thus their production and the subsequent backreaction is important at very early stages of the tachyon decay. I'm studying whether the backreaction of the massive closed string modes resolves the space-like singularity in the supergravity description of the unstable D-brane decay.
Recently, Kachru et.al, made an important progress towards constructing four dimensional de-Sitter vacua in string theory with finite Newton's constant. Their construction requires extended objects of string theory (D-branes), and incorporation of nonperturbative (though under control) string theory corrections. I am further exploring these constructions, in particular attempting to construct specific string theory models that combine inflation and present day acceleration.
One of the most mysterious objects of our Universe are black holes.
For one reason, they have thermodynamics unlike
that of a conventional physical system described by
quantum field theory. Specifically, the Bekenstein-Hawking
entropy formular suggests that the fundamental degrees of freedom
necessary to describe a black hole are characterized be a quantum
field theory with one fewer space dimensions. String theory
provided a satisfactory explanation for the thermodynamic properties
of certain black holes. In addition to basic black holes arising in General
Relativity, in string theory one encounters rather exotic black holes.
We predicted and studied phase transitions
in a class of stringy black holes as realizations of strongly coupled
finite temperature phase transitions in gauge theories.
While the gross features of the transitions were explained,
some important characteristics (like the order of a transition,
its dynamical onset, and the
relation between confinement/deconfinement and chiral symmetry
breaking/restoration) were left open. The dual
string theory language is currently the only analytical
framework to study these phenomena. Their clear explanation
undoubtedly would improve our understanding of
strong interactions in Nature.
A closely related problem, in which string theory can actually benefit from the holographic dual description in terms of gauge theory is the problem of a black hole interior. An interior of a black hole has a space-like singularity whose resolution in general relativity (or string theory) is currently not understood. Following gauge/string theory correspondence, certain black holes have a dual realization as finite temperature four-dimensional gauge theories in the deconfining phase. Consequently, studying the thermodynamics of these gauge theories should allow us to probe the physics behind the black hole horizon.