We review our recent work on solitons in the Higgs phase. We use U (NC) gauge theory with
NF Higgs scalar fields in the fundamental representation, which can be extended to possess …

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-
Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet …

In the last decade methods and techniques based on supersymmetry have provided deep
insights in quantum chromodynamics and other non-supersymmetric gauge theories at …

These lectures cover aspects of solitons with focus on applications to the quantum dynamics
of supersymmetric gauge theories and string theory. The lectures consist of four sections …

When instantons are put into the Higgs phase, vortices are attached to instantons. We
construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U …

We clarify relations among topological solitons in various dimensions: a domain wall, non-
Abelian vortex, magnetic monopole, and Yang-Mills instanton, together with a (non-Abelian) …

We present a weak-coupling Yang-Mills model supporting non-Abelian magnetic flux tubes
and non-Abelian confined magnetic monopoles. In the dual description the magnetic flux …

A bstract We study various composites of global solitons consisting of domain walls, strings,
and monopoles in linear O (N) models with N= 2 and 3. Spontaneous symmetry breaking …

We make a detailed study of the moduli space of winding number two (k= 2) axially
symmetric vortices (or equivalently, of coaxial composite of two fundamental vortices) …

We consider a benchmark bulk theory in four dimensions: N= 2 supersymmetric QCD with
the gauge group U (N) and N f flavors of fundamental matter hypermultiplets (quarks). The …