2D quantum gravity from quantum entanglement

In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.     

Taming the cosmological constant in 2D causal quantum gravity with topology change

As shown in previous work, there is a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of causal dynamical triangulations in two dimensions. In this paper we derive a complete analytical solution of the quantum continuum dynamics of this model, obtained uniquely by means of a double-scaling limit. We show that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the four-dimensional Euclidean path integral. Remarkably, in the continuum limit we obtain a finite spacetime density of microscopic wormholes without assuming fundamental discreteness. This shows that one can in principle make sense of a gravitational path integral which includes a sum over topologies, provided suitable causality restrictions are imposed on the path integral histories.     

Entropy of random coverings and 4D quantum gravity

We discuss the counting of minimal geodesic ball coverings of n-dimensional (n ≥ 3) riemannian manifolds of bounded geometry, fixed Euler characteristic, and Reidemeister torsion in a given representation of the fundamental group. This counting bears relevance to the analysis of the continuum limit of discrete models of quantum gravity. We establish the conditions under which the number of coverings grows exponentially with the volume, thus allowing for the search of a continuum limit of the corresponding discretized models. The resulting entropy estimates depend on representations of the fundamental group of the manifold through the corresponding Reidemeister torsion. We discuss the sum over inequivalent representations both in the two-dimensional and in the four-dimensional case. Explicit entropy functions as well as significant bounds on the associated critical exponents are obtained in both cases.     

Curved space-time formulation of the conformal sector for 4D quantum gravity

Developing the approach by Antoniadis and mottola to 4D quantum gravity, we investigate the dynamics of the conformal factor of 4D induced gravity in arbitrary curved background. The one-loop -functions are calculated in infrared stable fixed point where the effective scalar theory is multiplicatively renormalized.     

Graph invariants of Vassiliev type and application to 4D quantum gravity

We consider graph invariants of Vassiliev type extended by the quantum group link invariants. When they are expanded byx whereq=e ^x , the expansion coefficients are known as the Vassiliev invariants of finite type. In the present paper, we define tangle operators of graphs given by a functor from a category of colored and oriented graphs embedded into a 3-space to a category of representations of the quasi-triangular ribbon Hopf algebra extended byU _q (sl(2),C)), which are subject to a quantum group analog of the spinor identity. In terms of them, we obtain the graph invariants of Vassiliev type expressed to be identified with Chern Simons vacuum expectation values of Wilson loops including intersection points. We also consider the 4d canonical quantum gravity of Ashtekar. It is verified that the graph invariants of Vassiliev type satisfy constraints of the quantum gravity in the loop space representation of Rovelli and Smolin.This is not the author's present address.     

Inflation from quantum gravity

A model for inflation based on a quantum gravity scenario is presented. The process allows inflation of a Planck size bubble to the observed universe.     

Einstein gravity emerging from quantum Weyl gravity

We advocate a conformal invariant world described by the sum of the Weyl, Dirac, and Yang-Mills action. Quantum fluctuations bring back Einstein gravity so that the long-distance phenomenology is as observed. Formulas for the induced Newton's constant and Eddington's constant are derived in quantized Weyl gravity. We show that the analogue of the trace anomaly for the Weyl action is structurally similar to that for the Yang-Mills action.     

3D quantum gravity and effective noncommutative quantum field theory

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.     

Unexpected spin-off from quantum gravity

We propose a novel way of investigating the universal properties of spin systems by coupling them to an ensemble of causal dynamically triangulated lattices, instead of studying them on a fixed regular or random lattice. Somewhat surprisingly, graph-counting methods to extract high- or low-temperature series expansions can be adapted to this case. For the two-dimensional Ising model, we present evidence that this ameliorates the singularity structure of thermodynamic functions in the complex plane, and improves the convergence of the power series.     

Half-integral spin from quantum gravity

For a certain class of three-manifolds, the angular momentum of an asymptotically flat quantum gravitational field can have half-integral values. In the absence of a full theory of quantum gravity, this result relies on a set of apparently natural assumptions governing the kinematics of such a theory. A key feature is that state vectors are in general invariant only under asymptotically trivial diffeomorphisms that can be continuously deformed to the identity. Angular momentum is associated with diffeomorphisms that look asymptotically like rotations; and the question of whether half-integral values occur depends on whether the diffeomorphism associated with a 2 rotation is itself deformable to the identity.This essay received the fourth award from the Gravity Research Foundation for the year 1981-Ed.     

Physics with nonperturbative quantum gravity: Radiation from a quantum black hole

We study quantum gravitational effects on black hole radiation, using loop quantum gravity. Bekenstein and Mukhanov have recently considered the modifications caused by quantum gravity on Hawking's thermal black-hole radiation. Using a simple ansatz for the eigenstates of the area, they have obtained the intriguing result that the quantum properties of geometry affect the radiation considerably, yielding a discrete spectrum, definitely non-thermal. Here, we replace the simple ansatz employed by Bekenstein and Mukhanov with the actual eigenstates of the area computed using loop quantum gravity. We derive the emission spectra, using a classic result in number theory by Hardy and Ramanujan. Disappointingly, we do not recover the Bekenstein-Mukhanov discrete spectrum, but — effectively — a continuum spectrum, consistent with Hawking's result. The Bekenstein-Mukhanov argument for the discreteness of the specrum is therefore likely to be an artifact of the ansatz, rather than a robust result (at least in its present kinematical version). The result is an example of concrete (although somewhat disappointing) application of nonperturbative quantum gravity.This essay received the second award from the Gravity Research Foundation, 1996—Ed.     

Fundamental decoherence from quantum gravity: a pedagogical review

We present a discussion of the fundamental loss of unitarity that appears in quantum mechanics due to the use of a physical apparatus to measure time. This induces a decoherence effect that is independent of any interaction with the environment and appears in addition to any usual environmental decoherence. The discussion is framed self consistently and aimed to general physicists. We derive the modified Schrödinger equation that arises in quantum mechanics with real clocks and discuss the theoretical and potential experimental implications of this process of decoherence.     

Graviton propagator from background-independent quantum gravity

We study the graviton propagator in Euclidean loop quantum gravity. We use spin foam, boundary-amplitude, and group-field-theory techniques. We compute a component of the propagator to first order, under some approximations, obtaining the correct large-distance behavior. This indicates a way for deriving conventional spacetime quantities from a background-independent theory.     

An anomaly associated with 4-dimensional quantum gravity

We compute the functional determinant quotient (detP _h )/(detP _g ) for the Paneitz operatorP in conformally related Riemannian metricsg, h, and discuss related positivily questions.     

Emergence of a small world from local interactions: modeling acquaintance networks

How do we make acquaintances? A simple observation from everyday experience is that often one of our acquaintances introduces us to one of his or her acquaintances. Such a simple triangle interaction may be viewed as the basis of the evolution of many social networks. Here, it is demonstrated that this assumption is sufficient to reproduce major nontrivial features of social networks: short path length, high clustering, and scale-free or exponential link distributions.     

Euclidean quantum gravity on a lattice

We construct a number of related euclidean lattice formulations of quantum gravity. The first version incorporates a path integral over discrete manifolds built out of four-cubes embedded in a higher dimensional flat hypercubic lattice. We show this expression is equal to a corresponding path integral in a local lattice field theory. The field theoretic path integral diverges and lacks a satisfactory vacuum state. This divergence can be interpreted as a consequence of a divergent phase space available for topological fluctuations in the four-manifolds of the original path integral. A modified version of the path integral over manifolds converges. We construct a Schrödinger equation and hamiltonian for the modified theory. The hamiltonian is self-adjoint, but as a result of the large phase space available for topological fluctuations, the hamiltonian's spectrum is probably not bounded from below. We show briefly how the flat enveloping space—time can be removed from most of the theories we present and how matter fields can be included.     

Classical general relativity derived from quantum gravity

The existence of long range macroscopic attractive forces between masses implies the existence of a mediating helicity ± 2 particle in special relativistic quantum particle theory. It is shown that this fact alone, without assuming the existence of an underlying tensor field, uniquely determines the long wavelength structure of quantum gravitation to be that of Einstein's theory. This equivalence is shown by deriving, from the Ward identities associated with the graviton propagator, the tree graph structure of the graviton-graviton and graviton-matter interaction and establishing that the classical Einstein action is the generating functional. Some properties of closed loop effects are also exhibited.