Can gravity appear due to polarization of instantons in the SO(4) gauge theory?

TL;DR

This paper proposes that gravity can emerge from a polarized vacuum state of an SO(4) gauge theory, where instantons induce a long-range interaction equivalent to general relativity.

Contribution

It introduces a novel mechanism where polarized instantons in an SO(4) gauge theory give rise to gravitational phenomena, linking gauge theory vacuum polarization to gravity.

Findings

Effective action matches Einstein-Hilbert action

Gravitational waves as gauge field modes

Newton constant related to instanton density

Abstract

Conventional non-Abelian SO(4) gauge theory is able to describe gravity provided the gauge field possesses a specific polarized vacuum state. In this vacuum the instantons and anti-instantons have a preferred direction of orientation. Their orientation plays the role of the order parameter for the polarized phase of the gauge field. The interaction of a weak and smooth gauge field with the polarized vacuum is described by an effective long-range action which is identical to the Hilbert action of general relativity. In the classical limit this action results in the Einstein equations of general relativity. Gravitational waves appear as the mode describing propagation of the gauge field which strongly interacts with the oriented instantons. The Newton gravitational constant describes the density of the considered phase of the gauge field. The radius of the instantons under consideration is comparable with the Planck radius.