Skyrmion

In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a topologically stable field configuration of a certain class of non-linear sigma models. It was originally proposed as a model of the nucleon by Tony Skyrme in 1962. As a topological soliton in the pion field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid state physics, as well as having ties to certain areas of string theory. In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a topologically stable field configuration of a certain class of non-linear sigma models. It was originally proposed as a model of the nucleon by Tony Skyrme in 1962. As a topological soliton in the pion field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid state physics, as well as having ties to certain areas of string theory. Skyrmions as topological objects are important in solid state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin 'hedgehog' (in the field of micromagnetics: out of a so-called 'Bloch point' singularity of homotopy degree +1) by a stereographic projection, whereby the positive north-pole spin is mapped onto a far-off edge circle of a 2D-disk, while the negative south-pole spin is mapped onto the center of the disk. In a spinor field such as for example photonic or polariton fluids the skyrmion topology corresponds to a full Poincaré beam (which is, a quantum vortex of spin comprising all the states of polarization). Skyrmions have been reported, but not conclusively proven, to be in Bose-Einstein condensates, superconductors, thin magnetic films and in chiral nematic liquid crystals. As a model of the nucleon, the topological stability of the Skyrmion can be interpreted as a statement that the baryon number is conserved; i.e. that the proton does not decay. The Skyrme Lagrangian is essentially a one-parameter model of the nucleon. Fixing the parameter fixes the proton radius, and also fixes all other low-energy properties, which appear to be correct to about 30%. It is this predictive power of the model that makes it so appealing as a model of the nucleon. Hollowed-out skyrmions form the basis for the chiral bag model (Chesire cat model) of the nucleon. Exact results for the duality between the fermion spectrum and the topological winding number of the non-linear sigma model have been obtained by Dan Freed. This can be interpreted as a foundation for the duality between a QCD description of the nucleon (but consisting only of quarks, and without gluons) and the Skyrme model for the nucleon. The skyrmion can be quantized to form a quantum superposition of baryons and resonance states. It could be predicted from some nuclear matter properties. In field theory, skyrmions are homotopically non-trivial classical solutions of a nonlinear sigma model with a non-trivial target manifold topology – hence, they are topological solitons. An example occurs in chiral models of mesons, where the target manifold is a homogeneous space of the structure group where SU(N)L and SU(N)R are the left and right chiral symmetries, and SU(N)diag is the diagonal subgroup. In nuclear physics, for N=2, the chiral symmetries are understood to be the isospin symmetry of the nucleon. For N=3, the isoflavor symmetry between the up, down and strange quarks is more broken, and the skyrmion models are less successful or accurate. If spacetime has the topology S3×R, then classical configurations can be classified by an integral winding number because the third homotopy group