We construct new classes of vortexlike solutions of the $C{P}^N$ model in ($3+1$) dimensions and discuss some of their properties. These solutions are obtained by generalizing to ($3+1$) dimensions the techniques well established for the two-dimensional $C{P}^N$ models. We show that as the total energy of these solutions is infinite, they describe evolving vortices and antivortices with the energy density of some configurations varying in time. We also make some further observations about the dynamics of these vortices.

• Received 31 August 2011

DOI:https://doi.org/10.1103/PhysRevD.84.085022