p-Branes from Generalized Yang–Mills Theory

We consider the reduced, quenched version of a generalized Yang–Mills action in 4k-dimensional spacetime. This is a new kind of matrix theory which is mapped through the Weyl–Wigner–Moyal correspondence into a field theory over a non-commutative phase space. We show that the “classical” limit of this field theory is encoded into the effective action of an open, (4k−1)-dimensional, bulk brane enclosed by a dynamical, Chern–Simons type, (4k− 2)-dimensional, boundary brane. The bulk action is a pure volume term, while the boundary action carries all the dynamical degrees of freedom.