The Generalization of Chern-Simons Current and the Topological Tensor Current of p-Branes

Abstract

To make the gauge field theory foundation of the topological current of p-branes introduced in our previous work, we present a novel topological tensor current in SO(N ) gauge field theory. This non-Abelian gauge field tensor current is the straightforward generalization of the Chern-Simons topological current of strings. By making use of the SO(N ) gauge potential decomposition theory and the φ-mapping topological current theory, it is proved that the p-brane is created at every isolated zero of the Clifford vector field − → φ (x) and the charges carried by p-branes are topologically quantized and labelled by the winding number of the φ-mapping.