Quantum Gravity on the Lattice

I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I cover the general methods and goals of the lattice approach. An underlying theme is the attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral quantum gravity, as derived from the non-trivial ultraviolet fixed point scenario. I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton's costant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length).Comment: 63 pages, 12 figure

Ultraviolet Divergences and Scale-Dependent Gravitational Couplings

I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely unrelated non-perturbative approaches, and how it relates to the vacuum state of quantum gravity, and specifically to the running of $G$. One distinctive feature of the new fixed point is the emergence of a second genuinely non-perturbative scale, analogous to the scaling violation parameter in non-abelian gauge theories. I argue that it is natural to identify such a scale with the small observed cosmological constant, which in quantum gravity can arise as a non-perturbative vacuum condensate. (Plenary Talk, 12-th Marcel Grossmann Conference on Recent Developments in General Relativity, Astrophysics and Relativistic Field Theories, UNESCO Paris, July 12-18, 2009).Comment: 24 pages, 3 figure

Inconsistencies from a Running Cosmological Constant

We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the non-local effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem.Comment: 34 pages. Typos fixed, references added, one section expande

Composite Leptons at the LHC

In some models of electro-weak interactions the W and Z bosons are considered composites, made up of spin-one-half subconstituents. In these models a spin zero counterpart of the W and Z boson naturally appears, whose higher mass can be attributed to a particular type of hyperfine spin interaction among the various subconstituents. Recently it has been argued that the scalar state could be identified with the newly discovered Higgs (H) candidate. Here we use the known spin splitting between the W/Z and H states to infer, within the framework of a purely phenomenological model, the relative strength of the spin-spin interactions. The results are then applied to the lepton sector, and used to crudely estimate the relevant spin splitting between the two lowest states. Our calculations in many ways parallels what is done in the SU(6) quark model, where most of the spin splittings between the lowest lying baryon and meson states are reasonably well accounted for by a simple color hyperfine interaction, with constituent (color-dressed) quark masses.Comment: 12 pages, footnotes added. Conforms to published versio

Vacuum Condensate Picture of Quantum Gravity

In quantum gravity perturbation theory in Newton's constant G is known to be badly divergent, and as a result not very useful. Nevertheless some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge-Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of G and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale xi in many ways analogous to the scaling violation parameter Lambda MSbar of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments.Comment: 72 pages, 7 figures. Typos fixed, references added. Conforms to published version. arXiv admin note: text overlap with arXiv:1506.0779

Newtonian Potential in Quantum Regge Gravity

We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice periodicity. We check that the continuum analog of this quantity reproduces the Newtonian potential in the weak field expansion. In the smooth anti-de Sitter-like phase, which is the only phase where a sensible lattice continuum limit can be constructed in this model, we attempt to determine the shape and mass dependence of the attractive potential close to the critical point in $G$. It is found that non-linear graviton interactions give rise to a potential which is Yukawa-like, with a mass parameter that decreases towards the critical point where the average curvature vanishes. In the vicinity of the critical point we give an estimate for the effective Newton constant.Comment: (47 pages), CERN-TH.7314/9