Crystal Manyfold Universes in AdS Space

TL;DR

This paper introduces crystal braneworld solutions in AdS space, forming complex lattice-like structures of branes that influence gravity and hierarchy generation, with potential observable signatures like Bloch wave graviton spectra.

Contribution

It presents new crystal braneworld configurations with intersecting branes in AdS space, expanding the Manyfold universe concept and exploring their phenomenological implications.

Findings

Existence of crystal braneworld solutions with various boundary conditions.

Bulk gravitons exhibit Bloch wave spectra with band structures.

Hierarchy generation depends on crystal volume and lattice spacing.

Abstract

We derive crystal braneworld solutions, comprising of intersecting families of parallel $n+2$-branes in a $4+n$-dimensional $AdS$ space. Each family consists of alternating positive and negative tension branes. In the simplest case of exactly orthogonal families, there arise different crystals with unbroken 4D Poincare invariance on the intersections, where our world can reside. A crystal can be finite along some direction, either because that direction is compact, or because it ends on a segment of $AdS$ bulk, or infinite, where the branes continue forever. If the crystal is interlaced by connected 3-branes directed both along the intersections and orthogonal to them, it can be viewed as an example of a Manyfold universe proposed recently by Arkani-Hamed, Dimopoulos, Dvali and the author. There are new ways for generating hierarchies, since the bulk volume of the crystal and the lattice spacing affect the 4D Planck mass. The low energy physics is sensitive to the boundary conditions in the bulk, and has to satisfy the same constraints discussed in the Manyfold universe. Phenomenological considerations favor either finite crystals, or crystals which are infinite but have broken translational invariance in the bulk. The most distinctive signature of the bulk structure is that the bulk gravitons are Bloch waves, with a band spectrum, which we explicitly construct in the case of a 5-dimensional theory.