Dualization of interacting theories including p=d−1 limiting cases

We study the vacuum partition functional Z J for a system of closed, bosonic p-branes coupled to p-forms in the limiting case: p+1= spacetime dimension. We suggest an extension of the duality transformation which can be applied to the limiting case even though no dual gauge potential exists in the conventional sense. The dual action thus obtained describes a current–current, static interaction within the bulk volume bounded by the d−1-brane. Guided by these results, we then construct a general expression for the parent Lagrangian that allows for a unified treatment of p-duality, even in the presence of external currents, using a first order formalism instead of the Bianchi identities. Finally, we show how this generalized dualization approach can accommodate the inclusion of a massive topological term in the parent action of an Abelian gauge theory.