New Type of String Solutions with Long Range Forces
  We explore the formation and the evolution of the string network in the
Abelian Higgs model with two complex scalar fields. A special feature of the
model is that it possesses a global $U(1)$ symmetry in addition to the $U(1)$
gauge symmetry. Both symmetries are spontaneously broken by the vacuum
expectation values of the two complex scalar fields. As we will show the
dynamics of the string network is quite rich compared with that in the ordinary
Abelian Higgs model with a single complex scalar field. In particular, we find
a new type of string solutions in addition to the conventional
Abrikosov-Nielsen-Olesen (local) string solution. We call this the
uncompensated string. An isolated uncompensated string has a logarithmic
divergent string tension as in the case of the global strings, although it is
accompanied by a non-trivial gauge field configuration. We also perform
classical lattice simulations in the $2+1$ dimensional spacetime, which
confirms the formation of the uncompensated strings at the phase transition. We
also find that most of the uncompensated strings evolve into the local strings
at later time when the gauge charge of the scalar field with a smaller vacuum
expectation value is larger than that of the scalar field with a larger vacuum
expectation value.
