Analytic approach to nonperturbative aspects of gauge theories

点击翻译按钮获取中文摘要

To have better understandings about nonperturbative aspects of guage field theories such as topological structure, constructive formulation, supersymmetry and quark confimenent it is helpful to develop analytical methods such as lattice gauge theory and effective field theory approaches.In lattice gauge theory approach we investigated chiral gauge theories based on lattice Dirac operator satisfying the Ginsparg-Wilson relation and made it clear the topological structure of lattice gauge fields (Fujiwara). Furthermore, we developeded a cohomological method to classify topological invariants. This tourned out to be useful to facilitate construction of chiral U(1) gauge theories on the lattice. Furthermore, we gave a concrete construction of the fermion measure for SU(2)xU(1) electroweak gauge theory on the lattice (Kikukawa). We also investigated lattice regularization of supersymmetric gauge theories and gave a lattice formulation of N=(2, 2) supersymmetric Yang-Mills theory in lower dimensions (Suzuki).The topological structure of abelian gauge theories on a periodic lattice can be understood from abelian gauge theory on a torus. We investigated Dirac operator zero-modes on a torus with a uniform magnetic background in arbitrary even dimensions (Fujiwara). The twisted boundary conditions for the wave functions can be resolved by making use of the geometric nature of the torus. The eigenvalue problem can be solved completely. We found that a set of zero-mode with a desired chirality appear and the degeneracy of the zero-modes can be understood from the magnetic translation symmetry of the background gauge field. Our results are perfectly consistent with the index theorem.In effective field theory approach we investigated Cho-Faddeev-Niemi decomposition of Yang-Mills fields and explained the mechanism of quark confinement by reformulating the theory in terms of the nonlinear field transformations (Kondo).