Gravity and instantons

TL;DR

This paper proposes a gauge theory framework where gravity emerges from a polarized vacuum state of non-Abelian gauge fields, with instantons playing a key role in reproducing Einstein's general relativity.

Contribution

It introduces a novel polarized vacuum phase in SO(4) gauge theory where instantons define an order parameter, leading to an effective action equivalent to the Einstein-Hilbert action.

Findings

Effective long-range action matches general relativity's Hilbert action.

Gravitons correspond to gauge field modes interacting with oriented instantons.

The gravitational constant relates to the density of the polarized phase.

Abstract

Conventional non-Abelian SO(4) gauge theory is able to describe gravity provided the gauge field possesses a specific polarized vacuum state in which the instantons have a preferred 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. Gravitons 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.