Spacetime as a membrane in higher dimensions

TL;DR

This paper explores the idea that our universe's spacetime could be a membrane embedded in higher dimensions, presenting solutions that demonstrate stability and localized fermionic modes within such a membrane.

Contribution

It introduces new higher-dimensional solutions where spacetime is modeled as a membrane, extending Melvin's flux tube and analyzing stability and fermion localization.

Findings

Membrane solutions generalize Melvin's flux tube.

Flat membranes are classically stable.

Zero modes of Dirac equation are confined to the membrane.

Abstract

By means of a simple model we investigate the possibility that spacetime is a membrane embedded in higher dimensions. We present cosmological solutions of d-dimensional Einstein-Maxwell theory which compactify to two dimensions. These solutions are analytically continued to obtain dual solutions in which a (d-2)-dimensional Einstein spacetime "membrane" is embedded in d-dimensions. The membrane solutions generalise Melvin's 4-dimensional flux tube solution. The flat membrane is shown to be classically stable. It is shown that there are zero mode solutions of the d-dimensional Dirac equation which are confined to a neighbourhood of the membrane and move within it like massless chiral (d-2)-dimensional fermions. An investigation of the spectrum of scalar perturbations shows that a well-defined mass gap between the zero modes and massive modes can be obtained if there is a positive cosmological term in (d-2) dimensions or a negative cosmological term in d dimensions.