Topological tensor current of (p)over-tilde-branes in the φ-mapping theory

We present a new topological tensor current of (p) over tilde-branes by making use of the phi-mapping theory. It is shown that the current is identically conserved and behaves as delta(<(phi)over right arrow>), and every isolated zero of the vector field <(phi)over right arrow>(x) corresponds to a "magnetic" (p) over tilde-brane. Using this topological current, the generalized Nambu action for multi (p) over tilde-branes is given, and the field strength F corresponding to this topological tensor current is obtained. It is also shown that the magnetic charges carried by (p) over tilde-branes are topologically quantized and labeled by Hopf index and Brouwer degree, the winding number of the phi mapping. (C) 2000 American Institute of Physics. [S0022-2488(00)01707-2].