The Non-Abelian Topological Gauge Field Theory of \tilde{p}-Branes

Abstract

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

15 pages