From $SL(5,\mathbb{R})$ Yang-Mills theory to induced gravity

TL;DR

This paper derives a gravity theory from a pure $SL(5, R)$ Yang-Mills framework, incorporating Einstein-Hilbert, cosmological, curvature squared, and torsion terms, with parameters linked to quantum effects.

Contribution

It introduces a novel approach connecting Yang-Mills theory to gravity, emphasizing the role of asymptotic freedom and Gribov parameters in determining gravitational constants.

Findings

Gravity emerges with a cosmological constant from Yang-Mills theory.

Newton and cosmological constants depend on energy scale and quantum parameters.

One-loop calculations support the theoretical framework.

Abstract

From pure Yang-Mills action for the $SL(5,\mathbb{R})$ group in four Euclidean dimensions we obtain a gravity theory in the first order formalism. Besides the Einstein-Hilbert term, the effective gravity has a cosmological constant term, a curvature squared term, a torsion squared term and a matter sector. To obtain such geometrodynamical theory, asymptotic freedom and the Gribov parameter (soft BRST symmetry breaking) are crucial. Particularly, Newton and cosmological constant are related to these parameters and they also run as functions of the energy scale. One-loop computations are performed and the results are interpreted.