| Outline of Final Research Achievements |
Interactions of the elementary particles are described by the gauge theories. The gauge fields, which are the fundamental object in the gauge theories, are obeyed by the principle that the gauge transformed gauge fields describe the same physics. This property leads to the topologically rich nature of the theory. In this research project, we investigated the topological properties of the strong interactions, and obtained new knowledge on the axion, which is the hypothetical particle to explain dark matter of the Universe. In particular, by the simulation of the lattice gauge theory, we published the results on how the axion mass changes in the early Universe. Also, the theoretical research on the topology in the gauge theory has been conducted, and obtained new results such as the relation between the topology and the quark confinement, and the relation to the duality among three dimensional gauge theories.
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