p-Branes from Generalized Yang-Mills Theory

TL;DR

This paper introduces a new matrix theory derived from a generalized Yang-Mills action in 4k dimensions, which maps to a non-commutative field theory and describes p-branes with boundary dynamics.

Contribution

It presents a novel formulation linking generalized Yang-Mills theories to p-branes via non-commutative geometry and boundary Chern-Simons actions.

Findings

The classical limit corresponds to an effective brane action.

Bulk action is a volume term, boundary carries dynamics.

Framework connects matrix models to brane physics.

Abstract

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.