The Non - Abelian Topological Gauge Field Theory of p̃ – Branes 1

By the generalization of Chern–Simons topological current and Gauss–BonnetChern theorem, the purpose of this paper is to make a non-Abelian gauge field theory foundation of the topological current of p̃-branes formulated in our previous work. Using φ–mapping topological current theory proposed by Professor Duan, we find that the topological p̃-branes are created at every isolated zero of vector field ~ φ(x). It is shown that the topological charges carried by p̃-branes are topologically quantized and labeled by Hopf index and Brouwer degree, i.e., the winding number of the φ–mapping. The action of topological p̃–branes is obtained and is just Nambu action for multistrings when D − d̃ = 2.