On the Structure of the Vacuum in Quantum Gravity: A View from the Asymptotic Safety Scenario

Alfio Bonanno

doi:10.3390/universe5080182

Abstract

Although the Asymptotic Safety scenario is one of the most promising approaches to quantum gravity, little attention has been devoted to the issue of the vacuum state. Higher derivative operators often appear on the ultraviolet critical surface around the non-Gaussian fixed point generating additional degrees of freedom which can render the standard vacuum unstable. When this happens, translation and rotational symmetries can be spontaneously broken and a new set of symmetries can show up at the level of the effective action. In this work, it will be argued that a “kinetic condensate” characterizes the vacuum state of asymptotically safe quadratic gravity theories. If this scenario is realized in the full theory, the vacuum state of gravity is the gravitational analogous to the Savvidy vacuum in Quantum Chromo-Dynamics (QCD).

Highlights

IntroductionThe complexity of the Quantum Chromo-Dynamics (QCD) vacuum state is reflected by nonperturbative contributions to h0|tr ( Fμν F μν )|0i and similar expectation values of more complicated gauge and Lorentz-invariant operators
In the Euclidean formulation of quantum gravity, the notion of a classical metric is formally defined by means of an expression of this kind h gμν i = ZD [ g] gμν e−S[ g], (1)where a suitable regularization prescription has been assumed
The flat spacetime emerges as a result of a coarse-graining on scales larger than the Planck length, but, at a fundamental level, the spacetime structure is characterized by a spontaneous breaking of the Lorentz symmetry

Summary

Introduction

The complexity of the QCD vacuum state is reflected by nonperturbative contributions to h0|tr ( Fμν F μν )|0i and similar expectation values of more complicated gauge and Lorentz-invariant operators. As the dimensionality of the ultraviolet critical manifold is not changed by the inclusion of the C2 term (which turns out to be a relevant one), it is possible that the value of α is stable against additional truncations. If this scenario is realized in the full theory, it is important to study its physical implications, its non-perturbative character poses serious technical difficulties. Albeit very preliminary, this is an interesting result because it can be considered as an indication that the true vacuum in an asymptotically safe quadratic gravity is not the perturbative one, but a “kinetic condensate” like in the conformal sector of R + R2 gravity (see [16])

Higher-Derivative Scalar Theory

Quadratic Gravity

Conclusions