Effective gravity from a quantum gauge theory in Euclidean space-time

TL;DR

This paper demonstrates how a quantum gauge theory in Euclidean space can be mapped to a modified gravity model, with mechanisms to generate Einstein-Hilbert and cosmological constant terms, linking quantum gauge fields to classical gravity.

Contribution

It introduces a novel mapping from a renormalizable gauge theory to a curved space-time with gravity-like dynamics, including a mechanism for symmetry breaking and effective gravitational action generation.

Findings

The gauge theory maps to a curved space-time with an effective metric.

A mechanism is proposed to generate Einstein-Hilbert and cosmological constant terms.

Solutions include de Sitter and Anti de Sitter space-times.

Abstract

We consider a $SO(d)$ gauge theory in an Euclidean $d$-dimensional space-time, which is known to be renormalizable to all orders in perturbation theory for $2\le{d}\le4$. Then, with the help of a space-time representation of the gauge group, the gauge theory is mapped into a curved space-time with linear connection. Further, in that mapping the gauge field plays the role of the linear connection of the curved space-time and an effective metric tensor arises naturally from the mapping. The obtained action, being quadratic in the Riemann-Christoffel tensor, at a first sight, spoils a gravity interpretation of the model. Thus, we provide a sketch of a mechanism that breaks the $SO(d)$ color invariance and generates the Einstein-Hilbert term, as well as a cosmological constant term, allowing an interpretation of the model as a modified gravity in the Palatini formalism. In that sense, gravity can be visualized as an effective classical theory, originated from a well defined quantum gauge theory. We also show that, in the four dimensional case, two possibilities for particular solutions of the field equations are the de Sitter and Anti de Sitter space-times.