322 research outputs found
Combinatorial and topological phase structure of non-perturbative n-dimensional quantum gravity
We provide a non-perturbative geometrical characterization of the partition
function of -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 -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
- …