The visible, three-dimensional universe is restricted to an energetic field "membrane" (brane) inside a higher-dimensional space, called the bulk. Matter and forces like electromagnetism are confined to the brane, but gravity may spread out into the bulk.
A p-dimensional brane is called a "p-brane": a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one, etc. Strings can attach to branes, and the vibrations of these strings give rise to particles and forces, so branes act as the "framework" for these interactions.
D-branes are classified by their spatial dimension, which is one less than their p-dimension. A D0-brane is a single point, a D1-brane is a line, a D2-brane is a plane, and a D25-brane fills the highest-dimensional space in 26d string theory.
Branes are dynamical objects which can propagate through spacetime according to the laws of physics.
The LED model postulates that our 4d universe exists on a brane in a higher dimensional space. It is then suggested that the other forces of nature (the electromagnetic force, strong interaction, and weak interaction) operate within this membrane and its four dimensions, while the gravitational particle graviton can propagate across the extra dimensions. This would explain why gravity is very weak compared to the other fundamental forces.
A brane multiverse postulates that a universe exists on a brane which floats in a higher dimension. In this bulk, there are other membranes with their own universes. These universes can interact with one another, and when they collide, the violence and energy produced is more than enough to give rise to a Big Bang. The chaotic fluctuations of quantum foam might interact with branes, creating a substrate in which branes exist and move.
A mathematical proof of the holographic principle comes from the AdS/CFT correspondence (Anti-de Sitter/Conformal Field Theory):
- The Bulk (AdS): A 5-dimensional space where gravity exists.
- The Brane (CFT): A 4-dimensional boundary (like our universe) where quantum particles exist, but gravity does not.
- The Equivalence: The correspondence proves that the complex gravitational physics of the bulk is mathematically identical to the flat quantum physics on the brane. They are the same reality viewed from two different angles.
In other words, our universe (the brane) is the "film" on which the hologram is written, and the higher dimensions (the bulk) are the projection resulting from that code.