Center for Theoretical Studies: Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University

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Division of String Theory and Mathematics

It is known that there are four fundamental forces in Nature, namely the electromagnetic, strong, weak, and gravitational forces. For the three forces except for the gravitational one, the "Standard Model" has been constructed based on quantum gauge field theory, and many experimental results can now be explained in a unified way. On the other hand, for gravitational theory, although its classical physics can be very well described by general relativity, it has been a problem that it is not consistent with quantum gauge field theory. String theory aims to resolve this problem by postulating that all particles in Nature, including graviton, are actually various oscillation modes on a string. In the quest for the origin of matter and the Universe, it is of crucial importance to construct a consistent theory that unifies all the fundamental forces in Nature. String theory is currently regarded as the most promising candidate for such a unified theory.

String theory was originally proposed in the late 1960s for the purpose of explaining the physical phenomena related to hadrons (baryons and mesons). By now it is known that hadron physics is described by a gauge theory called quantum chromodynamics (QCD) but, since it was found in the middle 1970s that string theory can describe gravitons, string theory has been considered instead as a candidate for a unified theory. Since the 1980s, many remarkable results have been obtained not only by physicists but also by mathematicians, through ideas such as conformal field theory, mirror symmetry, and D-branes. However, in spite of all such developments, it is still very difficult to precisely reproduce the Standard Model from string theory. This is presumably because we do not yet fully understand the extremely rich mathematical structure of string theory.

Among the recent developments in string theory, our division focuses on the gauge theory-string theory correspondence. This is a surprising claim that two seemingly very different theories -- gauge theory and string theory (including gravity) -- are actually equivalent to each other. This correspondence is remarkable from the viewpoint of the unified theory but, in addition, it has aroused much interest because it enables us to compute physical quantities which are extremely difficult to compute otherwise. One of the projects our division is working on is the application of the correspondence to hadron physics. Models that can reproduce many properties of QCD have been constructed using the gauge theory-string theory correspondence and it has been confirmed that the correspondence is very useful also for understanding hadron physics. The goals of the project are further clarifications of hadron physics based on these models and improvement of the models to describe the actual QCD more accurately. On the other hand, the gauge theory-string theory correspondence is notable also because it predicts equalities which are mathematically quite unexpected. Our division studies the gauge theory-string theory correspondence by relating it to integrable systems with infinite dimensional symmetry and quantum topological invariants as mathematical structures of string theory. We also study generalization of light-cone string field theory and orbifold compactification of heterotic string theory, in order to elucidate the rich mathematical structure of string theory.

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