Field Theory and Gravity-foundation and applications

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Various properties in field theory and gravity were clarified.1. It is possible that there are both true vacuum and false vacuum in scalar field theory. It was shown in a series of papers that lump solutions, inside and outside of which are the false vacuum and the true vacuum, respectively, become stable provided there are fermions coupled to the scalar field inside the lumps. Yukawa interactions play an important role. These lumps can be produced in the early universe, or can be good candidates for dark matter observed now.2. It is found that in the Weinberg-Salam-Einstein theory there naturally arises a configuration in which Yang-Mills fields and Higgs fields intertwine each other, if the spatial topology of the universe is closed. As the universe expands, this configuration becomes unstable. In the course of the relaxation to more stable configurations large magnetic fields can be produced.3. In grand unified theory defined on orbifolds, dynamical rearrangement of gauge symmetry takes place through the Hosotani mechanism. Boundary conditions form equivalence classes. In each equivalence class the resultant physics is the same, irrespective of boundary conditons chosen, due to quantum effects. It is also proposed to select an equivalence class of boundary conditions which leads to the lowest energy density. In theminimal model, however, the symmetry of the standard model is not chosen.4. In string theory the spacetime dimensions are ten, but the observed dimensions are four. The six extra dimensions must guarantee the Weyl invariance in string theory. It is shown that there are nontrivial six-dimensional curved space in which the B field is nonvanishing.