Bosonic Fields in Crystal Manyfolds

TL;DR

This paper investigates how bosonic fields such as scalars, gauge, and Kalb-Ramond fields behave in a 1D crystal-like universe with intersecting membranes, revealing Bloch wave solutions and mass spectra dependent on dimensional parameters.

Contribution

It introduces a model of a crystal manyfold universe with intersecting membranes, analyzing field localization, wave functions, and mass spectra, including generalization to q-forms and their dependencies.

Findings

Wave functions are Bloch waves.

Zero-gap mass behavior is observed.

Mass spectra depend on dimension, q-form, and coupling.

Abstract

A chain-like or a 1D crystal-like universe made of intersecting membranes in extra dimensions in a Randall-Sundrum scenario is studied. A background gravitational metric satisfying the right boundary conditions is considered to study the localization of the scalar, gauge and Kalb-Ramond field. It is found that the wave function for the fields are Bloch waves. The mass modes equations are calculated allowing us to show the zero-gap mass behavior and the mass dispersion relation for each field. Finally we generalize all these results and consider $q-$forms in the crystal membrane universe. We show that, depending to the dimension $D$, the form $q$ and the dilation coupling $\lambda$ the mass spectrum can be the same for the different bosonic field studied.