Quantum Gravity from Noncommutative Spacetime

Abstract

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative $\star$-algebra) of quantum gravity.

97 pages, to be published in J. Korean Phys. Soc

References in corpus (16)

• Dark Energy and Gravity
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Symmetry, Gravity and Noncommutativity
• Emergent Gravity from Noncommutative Spacetime
• N=4 Super Yang-Mills from the Plane Wave Matrix Model
• Cosmological solutions of emergent noncommutative gravity
• Gravity and the Structure of Noncommutative Algebras
• Emergent Spacetime and The Origin of Gravity
• Yang-Mills Instantons from Gravitational Instantons
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Towards A Background Independent Quantum Gravity
• Emergent Geometry from Quantized Spacetime
• On the Newtonian limit of emergent NC gravity and long-distance corrections
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• Gravity and its Mysteries: Some Thoughts and Speculations
• Emergent Spacetime and The Cosmological Constant

Cited by in corpus (16)

• Quantization of Emergent Gravity
• Holographic Dark Energy and Quantum Entanglement
• Bilocal fields and gravity
• Thermofield dynamics and Gravity
• Calabi-Yau manifolds from noncommutative Hermitian U(1) instantons
• Mirror Symmetry in Emergent Gravity
• Emergent Spacetime for Quantum Gravity
• Dark Energy and Dark Matter in Emergent Gravity
• Quantized Kähler Geometry and Quantum Gravity
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Emergent Spacetime and Cosmic Inflation
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence
• Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects
• Towards a T-dual Emergent Gravity
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes