Effective gravity from a quantum gauge theory in Euclidean spacetime

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 ≤ d ≤ 4. 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. * sobreiro@cbpf.br † vjose@cbpf.br

From SL(5, ℝ) Yang–Mills theory to induced gravity

“…Four-dimensional metric free gauge theories of gravities have been studied for almost four decades, see for instance [1,2,3,4,5,6,7,8]. This kind of theories are of great relevance on the construction of a quantum gravity model because spacetime deformation and equivalence principle are consequences of the dynamics of the theory, see [8,9,10,11]. In that sense, the usual incompatibilities between the principles of quantum filed theory and geometrodynamics are avoided.…”

“…To do this, a mass scale is necessary because the gauge connection has dimension 1 while the vierbein has dimension 0. Except in [8,9], only topological actions were considered [1,2,3,4,5,6]. In this case, the Higgs mechanism is employed in order to split the group and make the vierbein to emerge.…”

“…Alternative mechanisms to bring geometry from a gauge theory were discussed by some of the authors in [8,9,10,11]. Specifically, in [8], an analogy between quantum chromodynamics and gravity was established.…”

Induced gravity from gauge theories

“…When the Yang-Mills action is taken into account, the starting theory is already metric dependent, see for instance [26,27]. Only in [28], the Yang-Mills was considered independently of the metric. The Lorentz group was taken as the gauge group of a theory in flat spacetime.…”

Cosmology from a gauge induced gravity

“…In the wide range of emergent gravities, there are several articles about gauge theories which employ a physical mechanisms to "free" the geometrical degrees of freedom, see for instance [18,19,20,21,22,23,24,25,26]. As a general aspect, the gravities which are generated in this way are described in first order variables [27,28,29].…”