p-Branes Electric-Magnetic Duality and Stueckelberg/Higgs Mechanism: a Path-Integral Approach

TL;DR

This paper explores how gauge invariance breaking at p-brane boundaries can generate mass via a path-integral approach, and examines the impact of electric-magnetic duality on this mass mechanism.

Contribution

It introduces a novel path-integral method focusing on field strengths to analyze mass generation and duality in p-brane systems with boundaries.

Findings

Mass can be generated through boundary effects without Higgs mechanism.

Duality exchanges roles of bulk and boundary gauge fields.

Path-integral formulation simplifies duality analysis.

Abstract

We study the vacuum functional for a system of p-branes interacting with Maxwell fields of higher rank. This system represents a generalization of the usual electrodynamics of point particles, with one essential difference: namely, that the world-history of a p-brane, due to the spatial extension of the object, may possess a physical boundary. Thus, the objective of this study is twofold: first, we wish to exploit the breaking of gauge invariance due to the presence of a physical boundary, in order to generate mass as an alternative to the Higgs mechanism; second, we wish to investigate how the new mechanism of mass generation is affected by the duality transformation between electric and magnetic branes. The whole analysis is performed by using the path-integral method, as opposed to the more conventional canonical approach. The advantage of the path integral formulation is that it enables us to Fourier transform the field strength directly, rather than the gauge potential. To our knowledge, this field strength formulation represents a new application of the path integral method, and leads, in a straightforward way, to the dual representation of the vacuum functional. We find that the effect of the dual transformation is essentially that of exchanging the role of the gauge fields defined respectively on the " bulk'' and "boundary" of the p-brane history.