Higher-dimensional knotlike topological defects in local non-Abelian topological tensor currents Available to Purchase

We present the novel topological tensor currents to describe the infinitesimal thin higher-dimensional topological defects in the local $SO(n)$ gauge theory. The topological quantization of defects and the inner structure of the currents are obtained. As the generalization of Nielsen-Olesen local $U(1)$ field theory for Nambu string, the local $SO(n)$ gauge-invariant Lagrangian and the motion equation of the higher-dimensional topological defects are derived. Moreover, for closed defects, we study their important topological configuration, i.e., the higher-dimensional knotlike structures. Using the topological tensor currents and their preimages, we construct a series of metric independent integrals and prove their gauge independence. Similar to the helicity integral characterizing one-dimensional knotlike vortex filament, these topological invariants are evaluated to the generalized linking numbers of higher-dimensional knotlike defects.