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

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

2007-05-15

arxiv.org/abs/0705.2200v3

Class.Quant.Grav.24:4937-4953,2007

Physics

High Energy Physics

High Energy Physics - Theory

20 pages; Final version accepted for publication in Class.Quant.Grav

Scientific paper

10.1088/0264-9381/24/20/003

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.

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