Schwarzschild instanton in emergent gravity

Abstract

In the bottom-up approach of emergent gravity, we attempt to find symplectic gauge fields emerging from Euclidean Schwarzschild instanton, which is studied as electromagnetism defined on the symplectic space [Formula: see text]. Geometrical engineering with the emergent metric sets up the Seiberg–Witten map between commutative and non-commutative gauge fields, preparing the ground for the evaluation of topological invariants in terms of the underlying gauge theory quantities.