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 (85)

• Gauge Theory Correlators from Non-Critical String Theory
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Deformation quantization of Poisson manifolds, I
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• A Large-N Reduced Model as Superstring
• D-brane Approach to Black Hole Quantum Mechanics
• Gauge Theory on Noncommutative Spaces
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• A path integral approach to the Kontsevich quantization formula
• Don't Panic! Closed String Tachyons in ALE Spacetimes
• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Nonlinear Instantons from Supersymmetric p-Branes
• Noncommutative Geometry and Gravity
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Quantum Foam and Topological Strings
• Wilson Loops in Noncommutative Yang Mills
• Dual geometries for a set of 3-charge microstates
• 3-charge geometries and their CFT duals
• Symmetry, Gravity and Noncommutativity
• A Note on Background Independence in Noncommutative Gauge Theories, Matrix Model and Tachyon Condensation
• Nonabelian noncommutative gauge theory via noncommutative extra dimensions
• Topological strings on noncommutative manifolds
• Noncommutative Field Theories and Gravity
• Noncommutative Instantons and Twistor Transform
• Deformed Coordinate Spaces; Derivatives
• Noncommutative Yang-Mills from equivalence of star products
• Derivative corrections to D-brane actions with constant background fields
• Noncommutative gauge theory for Poisson manifolds
• The quantum structure of black holes
• An Exact Solution to Seiberg-Witten Equation of Noncommutative Gauge Theory
• *-Trek II: *_n Operations, Open Wilson Lines and the Seiberg-Witten Map
• Describing Curved Spaces by Matrices
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• Open Wilson Lines in Noncommutative Gauge Theory and Tomography of Holographic Dual Supergravity
• Twisted Bundle On Quantum Torus and BPS States in Matrix Theory
• Morita equivalence and T-duality (or B versus $\Theta$)
• Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
• The Lagrangian of a Self-Dual Gravitational Field as a Limit of the SDYM Lagrangian
• Exact Seiberg-Witten Map and Induced Gravity from Noncommutativity
• Derivative corrections to the D-brane Born-Infeld action: non-geodesic embeddings and the Seiberg-Witten map
• Gauge and Einstein Gravity from Non-Abelian Gauge Models on Noncommutative Spaces
• Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories
• Closed Strings Tachyons and Non-Commutative Instabilities
• Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory
• Space-Time Foam From Non-Commutative Instantons
• Seiberg-Witten Transforms of Noncommutative Solitons
• Ramond-Ramond Couplings of Noncommutative D-branes
• Instantons and Emergent Geometry
• Self-dual gravity and the chiral model
• Toda fields of SO(3) hyper-Kahler metrics and free field realizations
• On Self-Dual Gravity I
• Noncommutative Two Dimensional Gravities
• ADHM is Tachyon Condensation
• Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons
• Gravitational Instantons from Gauge Theory
• Derivative corrections to Dirac-Born-Infeld Lagrangian and non-commutative gauge theory
• On Open String Sigma-Model and Noncommutative Gauge Fields
• Noncommutative Electrodynamics
• Field Equations of Massless Fields in the New Interpretation of the Matrix Model
• D-brane Physics and Noncommutative Yang-Mills Theory
• ALE spaces from noncommutative U(1) instantons via exact Seiberg-Witten map
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Instantons in the U(1) Born-Infeld Theory and Noncommutative Gauge Theory
• A Note on the BPS Spectrum of the Matrix Model
• A Note on Gauge Invariant Operators in Noncommutative Gauge Theories and the Matrix Model
• Quantum Aspects of GMS Solutions of Noncommutative Field Theory and Large N Limit of Matrix Models
• Constraints on effective Lagrangian of D-branes from non-commutative gauge theory
• Comments on the Morita Equivalence
• More About Partition Function of Open Bosonic String in Background Fields and String Theory Effective Action
• On the Equivalence between Noncommutative and Ordinary Gauge Theories
• Graviton Propagators in Supergravity and Noncommutative Gauge Theory
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• Graviton Propagators on Fuzzy G/H
• Non-commutative Twistor Space
• On Relation Between Moyal and Kontsevich Quantum Products. Direct Evaluation up to the ${\hslash }^3$-Order
• Noncommutative Dirac-Born-Infeld Action for D-brane
• Applications of the Ashtekar gravity to four dimensional hyperkähler geometry and Yang-Mills Instantons
• Anti-self-dual Maxwell solutions on hyperkähler manifold and N=2 supersymmetric Ashtekar gravity
• Propagators in Noncommutative Instantons
• Further Remarks on the Chiral Model Approach to Self-Dual Gravity
• Issues on 3D Noncommutative Electromagnetic Duality
• New Description of Self-Dual Metrics

Cited by in corpus (73)

• Quantum Spacetime Phenomenology
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model
• On The Correspondence Between Noncommuative Field Theory And Gravity
• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• Fermions and Emergent Noncommutative Gravity
• Emergent gravity on covariant quantum spaces in the IKKT model
• Instantons and Emergent Geometry
• Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models
• Emergent Geometry and Quantum Gravity
• Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
• Noncommutative SO(2,3) gauge theory and noncommutative gravity
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Matrix Bases for Star Products: a Review
• Towards A Background Independent Quantum Gravity
• Higher-spin gravity and torsion on quantized space-time in matrix models
• Emergent Geometry from Quantized Spacetime
• Test of Emergent Gravity
• Quantum Gravity from Noncommutative Spacetime
• Quantum (Matrix) Geometry and Quasi-Coherent States
• An Efficient Representation of Euclidean Gravity I
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Quantization of Emergent Gravity
• Discrete torsion, de Sitter tunneling vacua and AdS brane: U(1) gauge theory on D4-brane and an effective curvature
• Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity
• Field Theory on Curved Noncommutative Spacetimes
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Notes on Emergent Gravity
• Quantum Kerr tunneling vacua on a $(D\bar{D}{)}_4$-brane: An emergent Kerr black hole in five dimensions
• Gravity theory on Poisson manifold with $R$-flux
• Noncommutative gravity and the relevance of the $\theta$-constant deformation
• Relating Noncommutative SO(2,3) Gravity to the Lorentz-Violating Standard-Model Extension
• On the Newtonian limit of emergent NC gravity and long-distance corrections
• Emergent gravity from relatively local Hamiltonians and a possible resolution of the black hole information puzzle
• Holographic Dark Energy and Quantum Entanglement
• Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Calabi-Yau manifolds from noncommutative Hermitian U(1) instantons
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Mirror Symmetry in Emergent Gravity
• Highly Effective Action from Large N Gauge Fields
• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• Intertwining noncommutativity with gravity and particle physics
• Scalar modes and the linearized Schwarzschild solution on a quantized FLRW space-time in Yang-Mills matrix models
• Non-commutativity from the double sigma model
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Ambiguities in the Seiberg-Witten Map and Emergent Gravity
• Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions
• Remarks on an Exact Seiberg-Witten map
• Quantized Kähler Geometry and Quantum Gravity
• 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
• Emergent Spacetime and Cosmic Inflation
• Dark Energy and Emergent Spacetime
• Contravariant geometry and emergent gravity from noncommutative gauge theories
• Towards Axiomatization and General Results on Strong Emergence Phenomena Between Lagrangian Field Theories
• Quantum Spacetime Pictures and Dynamics from a Relativity Perspective
• Mass generation from a non-perturbative correction: Massive NS-field and graviton in $(3+1)$-dimensions
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons
• Geometric torsion, 4-form, Riemann duals and Quintessence
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
• Quantum Spacetimes from General Relativity?
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
• An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories
• Towards a T-dual Emergent Gravity
• $U(1)$-Gauge Field Theories on $G_2$-Manifolds
• Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory