Schwarzschild Instanton in Emergent Gravity

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 $(M,\omega)$. 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.