  We review our recent works on solitons in U(Nc) gauge theories with Nf (>Nc)
Higgs fields in the fundamental representation, which possess eight
supercharges. The moduli matrix is proposed as a crucial tool to exhaust all
BPS solutions, and to characterize all possible moduli parameters. Since vacua
are in the Higgs phase, we find domain walls (kinks) and vortices as the only
elementary solitons. Stable monopoles and instantons can exist as composite
solitons with vortices attached. Webs of walls are also found as another
composite soliton. The moduli space of all these elementary as well as
composite solitons are found in terms of the moduli matrix. The total moduli
space of walls is given by the complex Grassmann manifold SU(Nf)/[SU(Nc)x
SU(Nf-Nc) x U(1)] and is decomposed into various topological sectors
corresponding to boundary conditions specified by particular vacua. We found
charges characterizing composite solitons contribute negatively (either
positively or negatively) in Abelian (non-Abelian) gauge theories. Effective
Lagrangians are constructed on walls and vortices in a compact form. The power
of the moduli matrix is illustrated by an interaction rule of monopoles,
vortices, and walls, which is difficult to obtain in other methods. More
thorough description of the moduli matrix approach can be found in our review
article (hep-th/0602170).
