Novel aspects in p-brane theories: Weyl-invariant light-like branes

We consider a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically light-like branes for any odd world-volume dimension, hence the acronym WILL-branes (Weyl-invariant Light-Like branes). We discuss in some detail the properties of WILL -brane dynamics which significantly differs from ordinary Nambu-Goto brane dynamics. We provide explicit solutions of WILL-membrane (i.e., p = 2) equations of motion in arbitrary D = 4 spherically symmetric static gravitational backgrounds, as well as in product spaces of interest in Kaluza-Klein context. In the first case we find that the WILL-membrane materializes the event horizon of the corresponding black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In the second 'Kaluza-Klein' context we find solutions describing WILL-branes wrapped around the internal (compact) dimensions and moving as a whole with the speed of light in the non-compact (space-time) dimensions. (authors)