Short distance freedom of quantum gravity

Fourth order derivative gravity in 3+1$3+1$ dimensions is perturbatively renormalizable and is shown to describe a unitary theory of gravitons in a limited coupling parameter space. The running gravitational constant which includes graviton contribution is computed. Generically, gravitational Newton?s constant vanishes at short distances in this perturbatively renormalizable and unitary theory.     

Asymptotic freedom in gauge theories and quantum gravity

Restrictions on the structure of a gauge theory which follow from the requirement of asymptotic freedom with respect to all coupling constants are studied. One-loop counterterms for renormalizable gravity with matter are computed. It is shown that for the group O(N), taking into account the contribution of quantum R²-gravity allows one to construct new, asymptotically free gauge theories with a reduced number of spinor multiplets. The results are compared with those obtained earlier for conformal gravity with matter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–41, January, 1990.The authors thank A. O. Barvinskii, I. L. Bukhbinder, and E. S. Fradkin for the discussions.     

Nonsingular black holes and degrees of freedom in quantum gravity

Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as other inhomogeneous models, are shown to be absent. Moreover, one sees how the classical reduction from infinitely many kinematical degrees of freedom to only one physical one, the mass, can arise, where aspects of quantum cosmology such as the problem of initial conditions play a role.     

Bimetric truncations for quantum Einstein gravity and asymptotic safety

In the average action approach to the quantization of gravity the fundamental requirement of “background independence” is met by actually introducing a background metric but leaving it completely arbitrary. The associated Wilsonian renormalization group defines a coarse graining flow on a theory space of functionals which, besides the dynamical metric, depend explicitly on the background metric. All solutions to the truncated flow equations known to date have a trivial background field dependence only, namely via the classical gauge fixing term. In this paper, we analyze a number of conceptual issues related to the bimetric character of the gravitational average action and explore a first nontrivial bimetric truncation in the simplified setting of conformally reduced gravity. Possible implications for the Asymptotic Safety program and the cosmological constant problem are discussed in detail.     

Evidence for asymptotic safety from lattice quantum gravity

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ～3/2 at short distance to ～4 at large distance scales, similar to results from causal dynamical triangulations. We argue that the short-distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.     

Heavy quarkonia and asymptotic freedom

We use semiclassical methods to discuss the scaling behaviour of quarkonium level splittings up to $\text{M(}\text{Q}\text{Q}\text{) = 200}\text{GeV}$. Special emphasis is laid on the effects of asymptotic freedom which are found to be essential for $\text{M(}\text{Q}\text{Q}\text{) ? 30}\text{GeV}$. The bound t$\text{t}$ system will almost look like the ? system except that $\text{R = ΔM (}{}^3\text{P}{}_2\text{?}{}^3\text{P}{}_1\text{)/ΔM(}{}^3\text{P}{}_1\text{?}{}^3\text{P}{}_0\text{)}$ is larger than 0.8. In the ? system R will already be close to 0.8.     

Meson hyperfine splittings and asymptotic freedom

Meson hyperfine splittings give empirical evidence that the short-ranged part of the potential binding quarks has the behavior expected of single color gluon exchange in an asymptotically free theory. Since the interaction of light confined quarks depends on only one length scale, while that of heavy confined quarks depends on two length scales, it is argued that the spin-dependent interactions are qualitatively different in the cases. Phenomenological evidence suggests that the spin-dependent interactions of light quarks are short-ranged only, while that of heavy quarks are predominantly long-ranged. It is proposed that a measurement of the F¹-F mass-difference will help clarify the nature of a possible long-ranged spin-spin interaction of strange quarks.     

Is asymptotic freedom enough?

Quantum field theories with strong interactions are usually required to be not only renormalizable but also asymptotically free, in order to avoid diseases such as the Landau ghost. In this paper we suggest an even more restrictive requirement: “asymptotic convergence”, which means that at high energies it must be possible to formulate a convergent resummation procedure for the perturbation expansion. Such a convergent resummation technique exists in QCD in the infinite color limit (N → ∞). We give an outline of a proof of this statement, and a brief account of possible consequences of our asymptotic convergence condition on model building.     

Regge behavior under asymptotic freedom

By a new method, we show that the asymptotically free ø₆³ field theory has a point of accumulation of Regge poles but no fixed cut. It is plausible that nonabelian gauge theories have an analogous singularity at j = 1.     

More comments on asymptotic freedom

The effective Coulomb interaction between sources with SU(2) color charge is reinvestigated at the one-loop order of perturbation theory. This quantity is shown to be formally identical with the effective Coulomb interaction between electric charges in the QED of massless, charged, vector fields with anomalous magnetic moments. This correspondence allows the one-loop Yang-Mills charge renormalization factor to be deduced from a knowledge of the size and origins of this quantity in massless scalar and spinor QED. Careful consideration of the analogy with QED suggests a mechanism for asymptotic freedom in the Feynman gauge.     

Bohm's quantum potentials and quantum gravity

A generally covariant theory, written in the spirit of Bohm's theory of quantum potentials, which applies to spinless, non interacting, gravitating systems, is formulated. In this theory the quantum state is coupled to the metric tensor g, and the effect of the quantum potential is absorbed in the geometry. At the same time, satisfies a covariant wave equation with respect to the very same g. This provides sufficient constraints to derive 11 coupled equations in the 11 unknowns: and the components of the metric tensor g_µv. The states of stable localized particles are identified, and vacuum-state solutions for both the Euclidean and the Lorentzian case are explicitly presented.     

Foundational problems in quantum gravity and quantum cosmology

The conventionalistically based instrumentalist epistemology and methodology underlying the various approaches to the quantization of gravity is contrasted with the operationally based logical analysis practiced by the founders of relativity theory and quantum mechanics in developing their respective disciplines. The foundational problems to which they give rise are described. Their origins are traced to instrumentalist practices which have been in the past the objects of criticisms by Dirac, Heisenberg, Born, and others, but which have nevertheless prevailed in relativistic quantum physics after the emergence of the conventional renormalization program. The operationally based premises of a recently developed geometro-stochastic approach to the quantization of gravity are analyzed. It is shown that their roots lie in the epistemology adopted by the founders of relativity theory and quantum mechanics, and that they reflect a conceptualization of quantum reality which offers the possibility of a resolution of the main foundational problems encountered by the other approaches to quantum gravity.     

Time and quantum gravity

The role of time in the interpretation of quantum mechanics and quantum gravity are analyzed, and changes to the form of quantum gravity to make it interpretable are suggested.     

Logics and quantum gravity

We consider the logic needed for models of quantum gravity, taking as our starting point a simple pregeometric toy model based on graph theory. First a discussion of quantum logic seen in the light of canonical quantum gravity is given, then a simple toy model is proposed and the logical structure underlying it exposed. It is then shown that this logic is nonclassical and in fact contains quantum logics as special cases. We then go on to show how Yang-Mills theory and quantum mechanics fits in. A single mathematical structure is proposed capable of containing all these subjects in a natural and elegant way. Causality plays an important role. The mere presence of a causal relation almost inevitably yields this kind of logic.     

Continuum-regularized quantum gravity

The recent continuum regularization ofd-dimensional Euclidean gravity is generalized to arbitrary power-law measure and studied in some detail as a representative example of coordinate-invariant regularization. The weak-coupling expansion of the theory illustrates a generic geometrization of regularized Schwinger-Dyson rules, generalizing previous rules in flat space and flat superspace. The rules are applied in a non-trivial explicit check of Einstein invariance at one loop: The cosmological counterterm is computed and its contribution is included in a verification that the graviton mass is zero.