Emergent Gravity from Noncommutative Spacetime

Abstract

We showed before that self-dual electromagnetism in noncommutative (NC) spacetime is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: Gravity can emerge from electromagnetism in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime. We elucidate in some detail why electromagnetism in NC spacetime should be a theory of gravity. In particular, we show that NC electromagnetism is realized through the Darboux theorem as a diffeomorphism symmetry G which is spontaneously broken to symplectomorphism H due to a background symplectic two-form $B_{\mu \nu }=(1/\theta {)}_{\mu \nu }$, giving rise to NC spacetime. This leads to a natural speculation that the emergent gravity from NC electromagnetism corresponds to a nonlinear realization G/H of the diffeomorphism group, more generally its NC deformation. We also find some evidences that the emergent gravity contains the structure of generalized complex geometry and NC gravity. To illuminate the emergent gravity, we illustrate how self-dual NC electromagnetism nicely fits with the twistor space describing curved self-dual spacetime. We also discuss derivative corrections of Seiberg-Witten map which give rise to higher order gravity.

50 pages; Cosmetic revision and updated references

References in corpus (9)

• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories
• Noncommutative Two Dimensional Gravities
• Field Equations of Massless Fields in the New Interpretation of the Matrix Model
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Graviton Propagators in Supergravity and Noncommutative Gauge Theory
• Issues on 3D Noncommutative Electromagnetic Duality
• New Description of Self-Dual Metrics

Cited by in corpus (25)

• Noncommutative SO(2,3) gauge theory and noncommutative gravity
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Quantum (Matrix) Geometry and Quasi-Coherent States
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Field Theory on Curved Noncommutative Spacetimes
• Notes on Emergent Gravity
• Holographic Dark Energy and Quantum Entanglement
• Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
• Calabi-Yau manifolds from noncommutative Hermitian U(1) instantons
• Intertwining noncommutativity with gravity and particle physics
• Non-commutativity from the double sigma model
• Remarks on an Exact Seiberg-Witten map
• Emergent 4D Gravity from Matrix Models
• Noncommutative Spacetime and Emergent Gravity
• Novel Ambiguities in the Seiberg-Witten Map and the Emergent Gravity
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Towards Axiomatization and General Results on Strong Emergence Phenomena Between Lagrangian Field Theories
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
• Towards a T-dual Emergent Gravity
• $U(1)$-Gauge Field Theories on $G_2$-Manifolds
• An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories
• Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory
• Quantum Spacetimes from General Relativity?
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes