1. Domain walls in non-linear sigma models and Nambu-Goto/Dirac-Born-Infeld action

I will explain some relation between domain walls and NG/DBI actions.
In the first part of my talk, I will explain recently found J-kink domain walls in D=4
massive CP1 sigma model. The J-kink domain wall is not static but stationary, and
characterized by conserved current J_\mu. It is classified into magnetic (J^2 < 0),
null (J^2=0), and electric (J^2 > 0) types. A low energy effective action of the domain
wall is known to be D=4 DBI action for a membrane, and we find that counterpart
of the J-kink is the membrane with constant magnetic field B and electric field E.
In the second part, I explain how we can get a low energy effective action on the
domain wall world-volume including higher derivative collections for a class of
extended CP^1 sigma model. We propose a simple way for deriving the effective
action which is a generalization of NG action including higher derivative collections
to all order.


2. 1/4 BPS boojums in N=2 supersymmetric gauge theories

N=2 supersymmetric gauge theories are nice playgrounds for studying BPS
solitons, instanton/monopole/vortex/domain wall. They are sometimes called
field theoretical D-branes because they share many properties with D-branes
in string theory. In this talk, I explain some aspects of composite solitons of
the vortex strings and domain walls with boojum appearing at the junction points.
This configuration has already studied in the literature, but so far only rough
approximate solutions have been known. In this study we numerically and
analytically solve the 1/4 BPS equation. The numerical and/or exact solutions
reveal rich phenomena inside/outside the domain walls. We find interesting
electromagnetic property of domain walls.


3. On vortex dynamics in 2 component BECs

Vortex dynamics in scalar BEC is well known: vortex and vortex show a
circular motion whereas vortex and anti-vortex show parallel linear motion.
Compared to this, much less has been known for dynamics of a small number
of vortices in 2 component BEC. In the first part of my talk, I  show how
two vortices in same/different condensates move. Then, I will introduce the
Rabi term which glues the two vortices. A vortex molecule has additional
dynamical modes, like presession and oscillation. I will show some numerical
analysis for dynamics of multiple vortex molecules. They are as if waltzing!