General Principles of Brane Kinematics and Dynamics

We consider branes as “points” in an infinite dimensional brane space M with a prescribed metric. Branes move along the geodesics of M. For a particular choice of metric the equations of motion are equivalent to the well known equations of the Dirac-Nambu-Goto branes (including strings). Such theory describes “free fall” in M-space. In the next step the metric of M-space is given the dynamical role and a corresponding kinetic term is added to the action. So we obtain a background independent brane theory: a space in which branes live is M-space and it is not given in advance, but comes out as a solution to the equations of motion. The embedding space (“target space”) is not separately postulated. It is identified with the brane configuration.