Baby Skyrmion strings

We consider two limiting cases of the 2+1 dimensional analog of the Skyrme model, where we show the existence of string-like solutions to the equations of motion. The model contains a conserved topological charge usually called the baryon number. Our strings are solitons which have a constant baryon number per unit length. In one limiting case, our configuration saturates a Bogomolnyi-type bound and is degenerate in energy per baryon with the baby Skyrmion which is the analog of the spherically symmetric Skyrmion soliton. Hence here the string is energetically stable. In the other limiting case these energies are still degenerate but neither saturates the corresponding Bogomolnyi-type bound. Here we find invariance under area preserving diffeomorphisms. Both cases are solvable analytically. For intermediate ranges of the parameters we provide numerical evidence of the existence of the string-like configurations in a region of the parameter space. We speculate that the string is classically stable here as the energy per length containing one baryon is less than the energy of an isolated baryon (radially symmetric “baby Skyrmion”).