Schwarzschild Instanton in Emergent Gravity

TL;DR

This paper explores how symplectic gauge fields emerge from the Euclidean Schwarzschild instanton within emergent gravity, linking geometry, gauge theory, and topological invariants.

Contribution

It introduces a method to derive symplectic gauge fields from Schwarzschild instantons and connects emergent metrics with the Seiberg-Witten map in a novel way.

Findings

Identification of symplectic gauge fields from Schwarzschild instanton

Establishment of the Seiberg-Witten map in this context

Evaluation of topological invariants via gauge theory quantities

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 $(M,\omega)$. 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.