The Universe as a topological defect

TL;DR

This paper demonstrates that four-dimensional Einstein's General Relativity can be derived from a gauge theory of the conformal group SO(4,2) via topological dimensional reduction involving a four-dimensional defect, leading to a gauged Wess-Zumino-Witten action.

Contribution

It introduces a novel derivation of Einstein's gravity from a topological gauge theory based on the conformal group, connecting topological defects to gravitational dynamics.

Findings

Einstein's equations emerge from a gauge theory of SO(4,2).

The action reduces to Einstein-Hilbert under a specific ansatz.

The coupling constant can take integer values with complex field continuation.

Abstract

Four-dimensional Einstein's General Relativity is shown to arise from a gauge theory for the conformal group, SO(4,2). The theory is constructed from a topological dimensional reduction of the six-dimensional Euler density integrated over a manifold with a four-dimensional topological defect. The resulting action is a four-dimensional theory defined by a gauged Wess-Zumino-Witten term. An ansatz is found which reduces the full set of field equations to those of Einstein's General Relativity. When the same ansatz is replaced in the action, the gauged WZW term reduces to the Einstein-Hilbert action. Furthermore, the unique coupling constant in the action can be shown to take integer values if the fields are allowed to be analytically continued to complex values.