Notes on Emergent Gravity

Abstract

Emergent gravity is aimed at constructing a Riemannian geometry from U(1) gauge fields on a noncommutative spacetime. But this construction can be inverted to find corresponding U(1) gauge fields on a (generalized) Poisson manifold given a Riemannian metric (M, g). We examine this bottom-up approach with the LeBrun metric which is the most general scalar-flat Kahler metric with a U(1) isometry and contains the Gibbons-Hawking metric, the real heaven as well as the multi-blown up Burns metric which is a scalar-flat Kahler metric on C^2 with n points blown up. The bottom-up approach clarifies some important issues in emergent gravity.

v3; 29 pages, minor clarifications for locally conformal symplectic structure and the origin of diffeomorphism, version to appear in JHEP

References in corpus (26)

• String Theory and Noncommutative Geometry
• Wilson Loops in Noncommutative Yang Mills
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Symmetry, Gravity and Noncommutativity
• Noncommutative Yang-Mills from equivalence of star products
• Emergent Gravity from Noncommutative Spacetime
• *-Trek II: *_n Operations, Open Wilson Lines and the Seiberg-Witten Map
• 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
• How Noncommutative Gauge Theories Couple to Gravity
• Exact Seiberg-Witten Map and Induced Gravity from Noncommutativity
• On The Correspondence Between Noncommuative Field Theory And Gravity
• Emergent Spacetime and The Origin of Gravity
• Instantons and Emergent Geometry
• Self-dual gravity and the chiral model
• Toda fields of SO(3) hyper-Kahler metrics and free field realizations
• Geometric Interpretation of Schwarzschild Instantons
• Gravitational Instantons from Gauge Theory
• Emergent Geometry and Quantum Gravity
• Hair in the Back of a Throat: Non-Supersymmetric Multi-Center Solutions from Kähler Manifolds
• ALE spaces from noncommutative U(1) instantons via exact Seiberg-Witten map
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Towards A Background Independent Quantum Gravity
• An Efficient Representation of Euclidean Gravity I
• 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

Cited by in corpus (13)

• Test of Emergent Gravity
• Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity
• Quantization of 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
• Ambiguities in the Seiberg-Witten Map and Emergent Gravity
• Quantized Kähler Geometry and Quantum Gravity
• Novel Ambiguities in the Seiberg-Witten Map and the Emergent Gravity
• Emergent Spacetime and Cosmic Inflation
• Bianchi-IX, Darboux-Halphen and Chazy-Ramanujan
• Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons
• Schwarzschild Instanton in Emergent Gravity
• Towards a T-dual Emergent Gravity