Lattice gauge fields topology uncovered by quaternionic {sigma}-model embedding

We investigate SU(2) gauge fields topology using new approach, which exploits the well known connection between SU(2) gauge theory and quaternionic projective {sigma}-models and allows to formulate the topological charge density entirely in terms of {sigma}-model fields. The method is studied in details and for thermalized vacuum configurations is shown to be compatible with overlap-based definition. We confirm that the topological charge is distributed in localized four-dimensional regions which, however, are not compatible with instantons. Topological density bulk distribution is investigated at different lattice spacings and is shown to possess some universal properties.