Test of Emergent Gravity

Abstract

In this paper we examine a small but detailed test of the emergent gravity picture with explicit solutions in gravity and gauge theory. We first derive symplectic U(1) gauge fields starting from the Eguchi-Hanson metric in four-dimensional Euclidean gravity. The result precisely reproduces the U(1) gauge fields of the Nekrasov-Schwarz instanton previously derived from the top-down approach. In order to clarify the role of noncommutative spacetime, we take the Braden-Nekrasov U(1) instanton defined in ordinary commutative spacetime and derive a corresponding gravitational metric. We show that the Kähler manifold determined by the Braden-Nekrasov instanton exhibits a spacetime singularity while the Nekrasov-Schwarz instanton gives rise to a regular geometry-the Eguchi-Hanson space. This result implies that the noncommutativity of spacetime plays an important role for the resolution of spacetime singularities in general relativity. We also discuss how the topological invariants associated with noncommutative U(1) instantons are related to those of emergent four-dimensional Riemannian manifolds according to the emergent gravity picture.

v3; 22 pages, version to appear in Phys. Rev. D

References in corpus (15)

• A Gravity Theory on Noncommutative Spaces
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Symmetry, Gravity and Noncommutativity
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Emergent Gravity from Noncommutative Spacetime
• Emergent Spacetime and The Origin of Gravity
• Yang-Mills Instantons from Gravitational Instantons
• Emergent Geometry and Quantum Gravity
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Towards A Background Independent Quantum Gravity
• Emergent Geometry from Quantized Spacetime
• An Efficient Representation of Euclidean Gravity I
• Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity
• Notes on Emergent Gravity
• Einstein Manifolds As Yang-Mills Instantons

Cited by in corpus (12)

• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity
• Quantization of Emergent Gravity
• Mirror Symmetry in Emergent Gravity
• 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
• Bianchi-IX, Darboux-Halphen and Chazy-Ramanujan
• Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons
• Generalization of Instanton-Induced Inflation and Dynamical Compactification
• Schwarzschild Instanton in Emergent Gravity
• Towards a T-dual Emergent Gravity