Derivation of a Unified Theory from the Holographic Principle

Abstract

Holographic principle and the related self-similarity symmetry are observed widely in nature. Research in black hole, string theory and quantum theory of gravity suggests that holographic principle can be an important symmetry for solving challenging problems in theoretical physics, such as finding the grand unification theory (GUT). In this paper, we derive a quantum theory incorporating the holographic principle by introducing the new concept and elementary information. The derived quantum action incorporating holographic principle, holographic action, turns out to be the generalized action encompassing string theory, general relativity and thermodynamics. This holographic quantum theory indicates that phenomena and laws of physics emerge from the holograms represented by the holographic action. Specifically, it predicts the following: (1) Elementary particles, gravity and gauge interactions and the classical equations of motion are the emergence of the hologram due to Poincaré symmetry, diffeomorphic symmetry and Weyl symmetry, respectively. (2) Dark matter and dark energy are the vibrations on the horizon scale of the universe. (3) Cosmological constant is calculated to be [Formula: see text] in Planck unit, in agreement with the cosmological constant deduced from astrophysical observation (4) The observed space-time is negatively curved if its dimension is greater than 4, positively curved if its dimension is less than 4, and flat if its dimension is 4. (5) It gives the mathematical formula to derive the entropy of black hole and study the internal dynamics of black hole. (6) It provides the mathematical framework to study the dynamics of spacetime compactification and the large hierarchy between Planck scale and electroweak scale. One may conclude that the holographic quantum theory based on holographic principle may be not only a GUT but also able to tackle some of the problems impossible to be addressed before.