Combinatorial and topological phase structure of non-perturbative n-dimensional quantum gravity

We provide a non-perturbative geometrical characterization of the partition function of $n$-dimensional quantum gravity based on a coarse classification of riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.Comment: 13 page

Boundary Conformal Field Theory and Ribbon Graphs: a tool for open/closed string dualities

We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.Comment: 40 pages, 7 figures; typos correcte

The geometry of dynamical triangulations

We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.Comment: 166 pages, Revtex (latex) fil

A non-perturbative Lorentzian path integral for gravity

A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time. For finite lattice volume, the associated transfer matrix is self-adjoint and bounded. The reflection positivity of the model ensures the existence of a well-defined Hamiltonian. The degenerate geometric phases found previously in dynamically triangulated Euclidean gravity are not present. The phase structure of the new Lorentzian quantum gravity model can be readily investigated by both analytic and numerical methods.Comment: 11 pages, LaTeX, improved discussion of reflection positivity, conclusions unchanged, references update

Correlational study and randomised controlled trial for understanding and changing red meat consumption: The role of eating identities

Rationale: The present studies aimed to contribute to the literature on psychological variables involved in reducing red meat consumption (RMC). Objective: Study 1 investigated whether the theory of planned behaviour (TPB), plus healthy-eating and meat-eating identities, could explain intentions to reduce RMC. Study 2 evaluated the effectiveness of an SMS text message intervention on self-monitoring to reduce RMC. Methods: In Study 1, data were collected daily using online food diaries for one week and a TPB questionnaire. Study 2 was a randomised controlled trial assessing pre– and post–RMC and TPB constructs by online food diaries and questionnaires over a one-week period. Participants were Italian undergraduates in each study (Study 1: N = 405; Study 2: N = 244). In Study 2, participants were randomly allocated to control and message condition groups. Participants in the message condition group received a daily SMS, which reminded them to monitor RMC, while participants in the control group did not receive any message. Only students who completed all measures were considered in the analyses (Study 1: N = 342; Study 2: N = 228). Results: Study 1 showed that affective and instrumental attitudes, perceived behavioural control, and meat-eating identity explained intentions to reduce RMC, while subjective norm, past behaviour, and healthy-eating identity did not. Study 2 showed that an SMS intervention was effective in increasing intentions and reducing RMC. Mediation analyses indicated partial serial mediation through healthy-eating and meat-eating identities and intentions. Conclusion: The present studies provide support for the predictive validity of TPB in explaining intentions to reduce RMC and for the efficacy of an SMS intervention targeting self-monitoring in reducing RMC. Findings confirmed the important role of eating identities in explaining intentions to reduce RMC and in changing this behaviour

The modular geometry of Random Regge Triangulations

We show that the introduction of triangulations with variable connectivity and fluctuating egde-lengths (Random Regge Triangulations) allows for a relatively simple and direct analyisis of the modular properties of 2 dimensional simplicial quantum gravity. In particular, we discuss in detail an explicit bijection between the space of possible random Regge triangulations (of given genus g and with N vertices) and a suitable decorated version of the (compactified) moduli space of genus g Riemann surfaces with N punctures. Such an analysis allows us to associate a Weil-Petersson metric with the set of random Regge triangulations and prove that the corresponding volume provides the dynamical triangulation partition function for pure gravity.Comment: 36 pages corrected typos, enhanced introductio

Entropy of random coverings and 4D quantum gravity

We discuss the counting of minimal geodesic ball coverings of $n$-dimensional 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.Comment: 54 pages, latex, no figure

Implementing holographic projections in Ponzano--Regge gravity

We consider the path-sum of Ponzano-Regge with additional boundary contributions in the context of the holographic principle of Quantum Gravity. We calculate an holographic projection in which the bulk partition function goes to a semi-classical limit while the boundary state functional remains quantum-mechanical. The properties of the resulting boundary theory are discussed.Comment: 20 pages, late