Sunggeun Lee, Raju Roychowdhury, Hyun Seok Yang
In this paper we examine a small but detailed test of the emergent gravity picture with explicit solutions in gravity and gauge theory. As a bottom-up approach of emergent gravity recently formulated by us, we derive symplectic U(1) gauge fields starting from the Eguchi-Hanson metric in four-dimensional Euclidean gravity and show that they precisely reproduce U(1) gauge fields of the Nekrasov-Schwarz instanton. As a top-down approach of emergent gravity, we take the U(1) instanton found by Braden and Nekrasov and derive a corresponding gravitational metric. We study the geometrical properties of the four-manifold determined by the Braden-Nekrasov U(1) instanton. It turns out that the gravitational metric of Braden-Nekrasov instanton exhibits a spacetime singularity although it becomes a regular solution without any physical singularity after a Kahler blow up from the gauge theory point of view. This result supports a wishful consensus that a spacetime singularity in general relativity can be resolved in a dual gauge theory description.
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http://arxiv.org/abs/1211.0207
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