Abstract:
We study four dimensional systems of global, axionic and local strings. By using the path integral formalism, we derive the dual formulation of these systems, where Goldstone bosons, axions and missive vector bosons are described by antisymmetric tensor fields, and strings appear as a source for these tensor fields. We show also how magnetic monopoles attached to local strings are described in the dual formulation. We conclude with some remarks.

Abstract:
We consider the dynamics of vortex strings and sound waves in superfluids in the phenomenological Landau-Ginzburg equation. We first derive the vortex equation where the velocity of a vortex is determined by the average fluid velocity and the density gradient near the vortex. We then derive the effective action for vortex strings and sound waves by the dual formulation. The effective action might be useful in calculating the emission rate of sound waves by moving vortex strings.

Abstract:
We investigate quantum tunneling in the theory of a complex scalar field with a global $U(1)$ symmetry when the charge density of the initial configuration does not vanish. We discuss the possible final configurations and set up the Euclidean path integral formalism to find the bubble nucleation and to study the bubble evolution. For the stationary path, or the bounce solution, in the Euclidean time, the phase variable becomes pure imaginary so that the charge density remains real. We apply this formalism to examples when the initial charge density is small. While the phase transition considered here occurs in zero temperature, the bubble dynamics is richly complicated, involving conserved charge, the sound wave and the supersonic bubble wall.

Abstract:
We review a progress in our understanding of the moduli space for an arbitrary number of BPS monopoles in a gauge theory with a group $G$ of rank $r$ that is maximally broken to $U(1)^r$. The derivation of the moduli space metric has been obtained from studying the low energy dynamics of well-separated dyons.

Abstract:
The self-dual systems are constrained and so are simpler to understand. In recent years there have been several studies on the self-dual Chern-Simons systems. Here I present a brief survey of works done by my collaborators and myself. I also discuss several questions related to these self-dual models.

Abstract:
We show that the BPS configurations of uniform field strength can be interpreted as those for sheets of infinite number of BPS magnetic monopoles, and found that the number of normalizable zero modes per each magnetic monopole charge is four. We identify monopole sheets as the intersecting planes of D3 branes. Similar analysis on self-dual instanton configurations is worked out and the number of zero modes per each instanton number is found to match that of single isolated instanton.

Abstract:
We review our recent work on the BPS magnetic monopoles and its relation to the electromagnetic duality in the N=4 supersymmetric Yang-Mills systems with an arbitrary gauge group. The gauge group can be maximally or partially broken. The low energy dynamics of the massive and massless magnetic monopoles are approximated by the moduli space metric. We emphasize the possible connection between the nature of the monopole moduli space with unbroken gauge group and the physics of mesons and baryons in QCD.

Abstract:
We investigate Yang-Mills theories with arbitrary gauge group on $R^3\times S^1$, whose symmetry is spontaneously broken by the Wilson loop. We show that instantons are made of fundamental magnetic monopoles, each of which has a corresponding root in the extended Dynkin diagram. The number of constituent magnetic monopoles for a single instanton is the dual Coxeter number of the gauge group, which also accounts for the number of instanton zero modes. In addition, we show that there exists a novel type of the $S^1$ coordinate dependent magnetic monopole solutions in $G_2,F_4,E_8$.

Abstract:
We investigate the role of massless magnetic monopoles in the N=4 supersymmetric Yang-Mills Higgs theories. They can appear naturally in the 1/4-BPS dyonic configurations associated with multi-pronged string configurations. Massless magnetic monopoles can carry nonabelian electric charge when their associated gauge symmetry is unbroken. Surprisingly, massless monopoles can also appear even when the gauge symmetry is broken to abelian subgroups.

Abstract:
Classical and quantum dynamics of two distinct BPS monopoles in the case of non-aligned Higgs fields are studied on the basis of the recently determined low energy effective theory. Despite the presence of a specific potential together with a kinetic term provided by the metric of a Taub-NUT manifold, an O(4) or O(3,1) symmetry of the system allows for a group theoretical derivation of the bound-state spectrum and the scattering cross section.