Narrow Results

We study the topological defects in the nonlinear O(3) sigma model in terms of the decomposition of U(1) gauge potential. Time-dependent baby skyrmions are discussed in the (2+1)-dimensional spacetime with the CP¹ field. Furthermore, we show that there are three kinds of topological defects–vortex lines, point defects and knot exist in the (3+1)-dimensional model, and their topological charges, locations and motions are determined by the ϕ-mapping topological current theory.

By making use of the background field method, we derive a novel reformulation of the Yang–Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang–Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically nontrivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.

We study particle states of quantum Hall ferromagnet from the viewpoint of the incompressible fluid description. It is shown that phase space of Chern–Simons matrix theory which is an effective theory for the incompressible fluid is equivalent to moduli space of vortex theory. According to this correspondence, elementary excitations in vortex theory are identified as particle states in quantum Hall ferromagnet, and thus we propose that a pure electron state is absent from the strong coupling region but only a composite particle state is present.