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

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.

arXiv comment19 pp. 3 figures. Title changed. Text with several changes. Latest version accepted in the IJMPD

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• About the (in)equivalence between holonomic versus non-holonomic theories of gravity
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• Homological aspects of topological gauge-gravity equivalence
• Static and spherically symmetric solutions in a scenario with quadratic curvature contribution