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

TL;DR

This paper develops a non-Abelian gauge field theory framework for tet-branes, linking topological charges to Hopf index and Brouwer degree, and deriving an action analogous to Nambu action for multistrings.

Contribution

It introduces a non-Abelian gauge theory foundation for tet-branes' topological current, connecting topological charges to -mapping invariants and deriving a Nambu-like action.

Findings

Topological tet-branes are created at zeros of a vector field.

Topological charges are quantized and labeled by Hopf index and Brouwer degree.

The derived action reduces to Nambu action for multistrings when D -  = 2.

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 $\phi $--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 $\vec \phi (x)$. 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 $\phi $--mapping. The action of topological $\tilde p$--branes is obtained and is just Nambu action for multistrings when $D- \tilde d=2$.