Gravitational Anderson Localization

TL;DR

This paper proposes a novel higher-dimensional gravity model where Anderson localization in a disordered brane crystal traps gravity, offering an alternative to curvature-based localization and addressing the hierarchy problem.

Contribution

It introduces a disordered brane crystal model for gravity localization via Anderson localization, distinct from curvature-based models like Randall-Sundrum.

Findings

Gravity is localized through Anderson localization in a disordered brane system.

The model allows for large extra dimensions with small curvature.

A continuum of four-dimensional theories with varying gravitational strengths is possible.

Abstract

We present a higher dimensional model where gravity is bound to a brane due to Anderson localization. The extra dimensions are taken to be a disordered crystal of branes, with randomly distributed tensions of order the fundamental scale. Such geometries bind the graviton and thus allow for arbitrarily large extra dimensions even when the curvature is small. Thus this model is quite distinct from that of Randall and Sundrum where localization is a consequence of curvature effects in the bulk. The hierarchy problem can be solved by having the standard model brane live a distance away from the brane on which the graviton is localized. The statistical properties of the system are worked out and it is shown that the scenario leads to a continuum of four dimensional theories with differing strengths of gravitational interactions. We live on one particular brane whose gravitational constant is G_N.