arXiv subjects

Daniele Oriti

Publications and source records attributed to Daniele Oriti.

At least 91 records · Page 5Linked to original sources

arXiv2016

The universe as a quantum gravity condensate

This is an introduction to the approach to the extraction of cosmological dynamics from full quantum gravity based on group field theory condensates. We outline its general perspective, which sees cosmology as the hydrodynamics of the fundamental quantum gravity degrees of freedom, as well as its concrete implementation within the group field theory formalism. We summarise recent work showing the emergence of a bouncing cosmological dynamics from a fundamental group field theory model, and provide a brief but complete survey of other results in the literature. Finally, we discuss open issues and directions for further research.

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arXiv2016

Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates

We study the effective cosmological dynamics, emerging as the hydrodynamics of simple condensate states, of a group field theory model for quantum gravity coupled to a massless scalar field and reduced to its isotropic sector. The quantum equations of motion for these group field theory condensate states are given in relational terms with respect to the scalar field, from which effective dynamics for spatially flat, homogeneous and isotropic space-times can be extracted. The result is a generalization of the Friedmann equations, including quantum gravity modifications, in a specific regime of the theory corresponding to a Gross-Pitaevskii approximation where interactions are subdominant. The classical Friedmann equations of general relativity are recovered in a suitable semi-classical limit for some range of parameters of the microscopic dynamics. An important result is that the quantum geometries associated with these GFT condensate states are non-singular: a bounce generically occurs in the Planck regime. For some choices of condensate states, these modified Friedmann equations are very similar to those of loop quantum cosmology.

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arXiv2016

Horizon entropy from quantum gravity condensates

We construct condensate states encoding the continuum spherically symmetric quantum geometry of an horizon in full quantum gravity, i.e. without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits an holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein--Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.

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arXiv2016

Generalised conservation laws in non-local field theories

We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalised conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalisation of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.

hep-th↗

arXiv2016

Functional Renormalisation Group analysis of Tensorial Group Field Theories on $\mathbb{R}^d$

Rank-d Tensorial Group Field Theories are quantum field theories defined on a group manifold $G^{\times d}$, which represent a non-local generalization of standard QFT, and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalisation analysis is crucial both for establishing their consistency as quantum field theories, and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalisation group flow of two simple classes of TGFTs, defined for the group $G=\mathbb{R}$ for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalisation group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.

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arXiv2015

Generalized quantum gravity condensates for homogeneous geometries and cosmology

We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction lends itself easily to be applied also to the case of spherically symmetric quantum geometries.

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arXiv2015

Group field theory as the 2nd quantization of Loop Quantum Gravity

We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.

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arXiv2015

Functional Renormalisation Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

We study a model of Tensorial Group Field Theory (TGFT) on $\mathbb{R}^3$ from the point of view of the Functional Renormalisation Group. This is the first attempt to apply a renormalisation procedure to a TGFT model defined over a non-compact group manifold. IR divergences (with respect to the metric on $\mathbb{R}$) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken. We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.

hep-th↗

arXiv2015

Dimensional flow in discrete quantum geometries

In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension $d$ at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number $0<α<d$, we find that the spatial spectral dimension reduces to $d_s \simeq α$ at small scales. The spatial Hausdorff dimension of such class of states varies between 1 and $d$, while the walk dimension takes the usual value $d_w=2$. Therefore, these quantum geometries may be considered as fractal only when $α=1$, where the "magic number" ${d_s}^{\rm spacetime}\simeq 2$ for the spectral dimension of space\emph{time}, appearing so often in quantum gravity, is reproduced as well. These results apply, in particular, to special superpositions of spin-network states in loop quantum gravity, and they provide more solid indications of dimensional flow in this approach.

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arXiv2015

Group field theories for all loop quantum gravity

Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the GFT formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

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arXiv2015

Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order

We study a just renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.

hep-th↗

arXiv2015

Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model

We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The system of FRG equations turns out to be non-autonomous in the RG flow parameter. This feature is explained by the existence of a hidden scale, the radius of the group manifold. We investigate in detail the opposite regimes of large cut-off (UV) and small cut-off (IR) of the FRG equations, where the system becomes autonomous, and we find, in both case, Gaussian and non-Gaussian fixed points. We derive and interpret the critical exponents and flow diagrams associated with these fixed points, and discuss how the UV and IR regimes are matched at finite N. Finally, we discuss the evidence for a phase transition from a symmetric phase to a broken or condensed phase, from an RG perspective, finding that this seems to exist only in the approximate regime of very large radius of the group manifold, as to be expected for systems on compact manifolds.

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arXiv2014

Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics

In the context of group field theory condensate cosmology, we clarify the extraction of cosmological variables from the microscopic quantum gravity degrees of freedom. We show that an important implication of the second quantized formalism is the dependence of cosmological variables and equations on the quantum gravitational atomic number N (number of spin network vertices/elementary simplices). We clarify the relation of the effective cosmological equations with loop quantum cosmology, understood as an effective (hydrodynamic-like) approximation of a more fundamental quantum gravity theory. By doing so, we provide a fundamental basis to the idea of lattice refinement, showing the dependence of the effective cosmological connection on N, and hence indirectly on the scale factor. Our results open a new arena for exploring effective cosmological dynamics, as this depends crucially on the new observable N, which is entirely of quantum gravitational origin.

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arXiv2014

Group Field Theory and Loop Quantum Gravity

We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a perspective on future developments.

gr-qc↗

arXiv2014

Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data

We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider. In particular, we study the asymptotic behavior of the path integral in the semi-classical limit. First, we compare the stationary phase equations in the classical limit for three different non-commutative structures corresponding to the symmetric, Duflo and Freidel-Livine-Majid quantization maps. We find that in order to unambiguously recover discrete geometric constraints for non-commutative metric boundary data through the stationary phase method, the deformation structure of the phase space must be accounted for in the variational calculus. When this is understood, our results demonstrate that the non-commutative metric representation facilitates a convenient semi-classical analysis of the Ponzano-Regge model, which yields as the dominant contribution to the amplitude the cosine of the Regge action in agreement with previous studies. We also consider the asymptotics of the ${\rm SU}(2)$ $6j$-symbol using the non-commutative phase space path integral for the Ponzano-Regge model, and explain the connection of our results to the previous asymptotic results in terms of coherent states.

gr-qc↗

arXiv2014

Spectral dimension of quantum geometries

The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them.

hep-th↗

arXiv2014

Melonic phase transition in group field theory

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.

hep-th↗

arXiv2014

Homogeneous cosmologies as group field theory condensates

We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

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