Emergent Geometry and Quantum Gravity

Abstract

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ωin terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.

Invited Review for Mod. Phys. Lett. A, 17 pages

References in corpus (4)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Emergent Gravity from Noncommutative Spacetime
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Emergent Gravity And The Cosmological Constant Problem

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• Quantization of Emergent Gravity
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity
• Discrete torsion, de Sitter tunneling vacua and AdS brane: U(1) gauge theory on D4-brane and an effective curvature
• Quantum Kerr tunneling vacua on a $(D\bar{D}{)}_4$-brane: An emergent Kerr black hole in five dimensions
• Notes on Emergent Gravity
• Gravity and compactified branes in matrix models
• Calabi-Yau manifolds from noncommutative Hermitian U(1) instantons
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• Ambiguities in the Seiberg-Witten Map and Emergent Gravity
• Emergent D-instanton as a source of Dark Energy
• Emergent Spacetime and Cosmic Inflation
• Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons
• Schwarzschild Instanton in Emergent Gravity
• $U(1)$-Gauge Field Theories on $G_2$-Manifolds
• Towards a T-dual Emergent Gravity