Dualization of Interacting Theories

Including $p=d-1$ Limiting Cases

S. Ansoldi¹

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

A. Aurilia²

Department of Physics, California State Polytechnic University

Pomona, CA 91768

E. Spallucci³

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

A. Smailagic⁴

Department of Physics, University of Osijek, Croatia,

Abstract:

We study the vacuum partition functional $Z\left[\, J\,\right]$ 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.