Infinite Conformal Symmetry and Emergent Chiral Fields of Topologically Nontrivial Configurations: from Yang-Mills-Higgs Theory to the Skyrme Model

In this manuscript, we discuss a remarkable phenomenon concerning nonlinear and nonintegrable field theories in (3 thorn 1) dimensions, living at finite density and possessing nontrivial topological charges and non-Abelian internal symmetries (both local and global). With suitable types of Ansatze, one can construct infinite-dimensional families of analytic solutions with nonvanishing topological charges (representing the baryonic number) labeled by both two integer numbers and by free scalar fields in (1 thorn 1) dimensions. These exact configurations represent (3 thorn 1)-dimensional topological solitons hosting (1 thorn 1)-dimensional chiral modes localized at the energy density peaks. First, we analyze the Yang-Mills-Higgs model, in which the fields depend on all the space-time coordinates (to keep alive the topological Chern-Simons charge), but in such a way to reduce the equations system to the field equations of two-dimensional free massless chiral scalar fields. Then, we move to the nonlinear sigma model, showing that a suitable Ansatz reduces the field equations to the one of a two-dimensional free massless scalar field. Then, we discuss the Skyrme model concluding that the inclusion of the Skyrme term gives rise to a chiral two-dimensional free massless scalar field (instead of a free massless field in two dimensions as in the nonlinear sigma model) describing analytically spatially modulated hadronic layers and tubes. The comparison of the present approach both with the instanton-dyon liquid approach and with lattice QCD is shortly outlined.