A Novel Framework for Quantum Gravity and Spacetime-Matter Symbiosis

The unification of quantum principles with Einstein's geometric conception of spacetime and gravity into a consistent theory of quantum gravity is one of the main open challenges at the foundations of modern theoretical physics. Among several approaches developed over the years, the two main candidates are string theory and loop quantum gravity (LQG). Both theories are characterized by their own achievements and open issues so that the solution to the problem of quantum gravity remains still elusive. In lack of experimental guidance, in order to make progress, it becomes important to single out common features shared by different approaches allowing to merge tools and ideas, thus providing indirect tests to potentially overcome current limitations. In this respect, one of the major recent developments is the so-called holographic principle and its string theory-based realization within the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, a conjectured duality between string theory in asymptotically AdS spacetime and a SU(N) gauge theory thought of as living on its conformal boundary. As such it provides a promising arena to look for possible connections between non-perturbative LQG and string theory non-perturbatively defined via its dual field theory. With this motivation in mind, in this thesis we focus on effective symmetry-reduced models for resolved cosmological and black hole singularities to which lot of effort has been devoted within the LQG community and their possible embedding within the AdS/CFT framework. First of all, we focus on the field theory signatures of the singularity resolution in the bulk of Kasner-AdS spacetimes and show via several examples of quantum corrected effective geometries that the finite-distance pole in the boundary two-point correlator previously interpreted as the holographic signature of the bulk singularity is smoothed out by quantum gravity effects. The time dependence of the boundary spacetime however prevents us from setting up an independent field theory computation to compare with the bulk gravity results. We move then to black hole (BH) singularities whose asymptotic boundary is Minkowski or AdS. Since no fully satisfactory effective LQG model is available already for the simplest static spherically symmetric case with zero cosmological constant, we consider the case of a 4-dimensional Schwarzschild BH as a necessary preparation for higher dimensional extensions to AdS BHs. New models based on new sets of canonical variables directly related to the Kretschmann scalar are thus introduced to take the onset of quantum effects under control, and the resulting quantum corrected spacetime structure is discussed in detail. A key ingredient of our analysis is the study of Dirac observables for the asymptotic ADM masses and their relation with admissible initial conditions for the effective dynamics compatibly with the requirement of a unique upper bound on curvature invariants resolving the central singularity. Finally, quantum corrections to thermodynamic quantities are also analyzed and, coming back to the original motivation of using LQG techniques for AdS/CFT, a possible extension to arbitrary dimensions and negative cosmological constant is sketched.

In many quantum gravity approaches, the cosmological constant is introduced by deforming the gauge group into a quantum group. In three dimensions, the quantization of the Chern-Simons formulation of gravity provided the first example of such a deformation. The Turaev-Viro model, which is an example of a spin-foam model, is also defined in terms of a quantum group. By extension, it is believed that in four dimensions, a quantum group structure could encode the presence of $\mathrm{\ensuremath{\Lambda}}\ensuremath{\ne}0$. In this article, we introduce by hand the quantum group ${\mathcal{U}}_{q}(\mathfrak{s}u(2))$ into the loop quantum gravity (LQG) framework; that is, we deal with ${\mathcal{U}}_{q}(\mathfrak{s}u(2))$-spin networks. We explore some of the consequences, focusing in particular on the structure of the observables. Our fundamental tools are tensor operators for ${\mathcal{U}}_{q}(\mathfrak{s}u(2))$. We review their properties and give an explicit realization of the spinorial and vectorial ones. We construct the generalization of the $\mathrm{U}(N)$ formalism in this deformed case, which is given by the quantum group ${\mathcal{U}}_{q}(\mathfrak{u}(N))$. We are then able to build geometrical observables, such as the length, area or angle operators, etc. We show that these operators characterize a quantum discrete hyperbolic geometry in the three-dimensional LQG case. Our results confirm that a quantum group structure in LQG can be a tool to introduce a nonzero cosmological constant into the theory. Our construction is both relevant for three-dimensional Euclidian quantum gravity with a negative cosmological constant and four-dimensional Lorentzian quantum gravity with a positive cosmological constant.

There are several approaches to quantum gravitational corrections of black hole thermodynamics. String theory and loop quantum gravity, by direct analysis on the basis of quantum properties of black holes, show that in the entropy–area relation the leading order correction should be of log-area type. On the other hand, generalized uncertainty principle (GUP) and modified dispersion relations (MDRs) provide perturbational framework for such modifications. Although both GUP and MDRs are common features of all quantum gravity scenarios, their functional forms are quantum gravity model dependent. Since both string theory and loop quantum gravity give more reliable solution of the black hole thermodynamics, one can use their results to test approximate results of GUP and MDRs. In this Letter, we find quantum corrected black hole thermodynamics in the framework of GUP and MDR and then we compare our results with string theory solutions. This comparison suggests severe constraints on the functional form of GUP and MDRs. These constraints may reflect characteristic features of ultimate quantum gravity theory.

Modern Canonical Quantum General Relativity

Of the different approaches to quantum gravity, the best developed, from the point of view of addressing the key theoretical questions a quantum theory of gravity must answer, is loop quantum gravity. While string theory appears to better address the issue of unification, at least so far, it fails to provide a background independent approach to the quantum mechanics of spacetime geometry-a necessary condition for any quantum theory of gravity. Moreover, many key conjectures remain unproven, including perturbative finiteness and consistency, which have not been demonstrated for any string theory past second order in perturbation theory. By contrast, loop quantum gravity appears to provide a consistent and finite background independent approach to quantum gravity. There is recent progress on several issues, including accounting for the black hole entropy [8], and giving a precise quantum mechanical description of the earliest phases of the evolution of the universe [9, 10]. Furthermore, it gives unique predictions of novel quantum gravitational phenomena, such as the discreteness of area, volume and other observables. However, in this new era of quantum gravity phenomenology, a quantum theory of gravity must pass a stricter test to be taken as a serious candidate: it must make unambiguous predictions for the upcoming experiments which probe the Planck scale. One way such predictions may arise is by modifications of the energymomentum relations of low energy physics, of the form,

The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounterbetween different approaches and different perspectives on the quantum-gravity problem. It contributedto a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program.There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed.In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field.Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics:• from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory,• from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime,• from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions.This volume provides an overview of these various topics, interesting for the specialist as well as accessibleto the newcomer. 4partially funded by CNRS PEPS /PTI ‘‘Metric aspect of noncommutative geometry: from Monge to Higgs’’

We study black hole radiation inside black holes within the framework of quantum gravity.First, we review on our previous work of a canonical quantization for a spherically symmetric geometry where one of the spatial coordinates is treated as the time variable, since we think of the interior region of a black hole.Based on this formalism, under physically plausible assumptions, we solve the Wheeler-De Witt equation inside the black hole, and show that the mass-loss rate of an evaporating black hole due to thermal radiation is equivalent to the result obtained by Hawking in his semi-classical approach.A remarkable point is that our assumptions make the momentum constraint coincide with the Hamiltonian constraint up to an irrelevant overall factor.Furthermore, for comparison, we solve the Wheeler-De Witt equation outside the black hole as well, and see that the mass-loss rate of an evaporating black hole has the same expression.The present analysis suggests that the black hole radiation comes from the black hole singularity.We also comment on the Birkhoff theorem in quantum gravity.

Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.

Recent cosmological observations of unprecented accuracy, by WMAP in particular, have established a `Standard Model' of cosmology, just as LEP established the Standard Model of particle physics. Both Standard Models raise open questions whose answers are likely to be linked. The most fundamental problems in both particle physics and cosmology will be resolved only within a framework for Quantum Gravity, for which the only game in town is string theory. We discuss novel ways to model cosmological inflation and late acceleration in a non-critical string approach, and discuss possible astrophysical tests.

In this paper we investigate the question of how spontaneous symmetry breaking works in the framework of loop quantum gravity and compare it to the results obtained in the case of the Proca field, where we were able to quantize the theory in loop quantum gravity without introducing a Higgs field. We obtained that the Hamiltonian of the two systems is very similar, the only difference is an extra scalar field in the case of spontaneous symmetry breaking. This field can be identified as the field that carries the mass of the vector field. In the quantum regime this becomes a well-defined operator, which turns out to be a self-adjoint operator with continuous spectrum. To calculate the spectrum we used a new representation in the case of scalar fields, which in addition enabled us to rewrite the constraint equations to a finite system of linear partial differential equations. This made it possible to solve part of the constraints explicitly.

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.

The two fundamental pillars of physics for over 100 years have been quantum theory and general relativity, but their unification at short distances remains elusive, both technically and conceptually. This work is a philosophical investigation of the second kind of problem, and in particular of the striking fact that in many approaches to ‘quantum gravity’ classical spacetime structures are not merely quantized, but arguably absent—so that spacetime is not merely a classical limit, but ‘emergent’. This issue is not only central to the problem of quantum gravity, but of deep significance for our philosophical understanding of physical reality, promising a conceptual revolution at least as profound as Einstein’s. We give an introduction to the question of spacetime emergence in general, for philosophers of metaphysics and science, and argue that spacetime functionalism explains how something non-spatiotemporal could ever appear as space and time. More technical chapters investigate the issue in detail for causal set theory, loop quantum gravity, and string theory, and the book also serves as a philosophical introduction to those theories for philosophers of physics. Our results help physicists clarify what new conceptual framework—not resting on space and time—may be necessary to achieve a theory of quantum gravity; and show philosophers how the world may not be spatiotemporal at root, and what kind of a world we might then live in.

With the SNOWMASS 2021 process in the US and the on-going European Strategy Report 2025, the field of elementary particle physics is undergoing detailed community evaluation, and the experimental particle physics program, which requires substantial public investment, is under scrutiny. We offer an assessment of the current experimental particle physics priorities from a string phenomenology point of view. String theory provides a perturbatively consistent framework for quantum gravity. String phenomenology aims to connect between string theory and observational data. String theory is a consistent theory of quantum gravity that contains the other fundamental constituents of matter and interactions. As all forms of energy couple to gravity, string theory provides a framework that reproduces the structures of the Standard Model of particle physics and gives rise to detailed physics scenarios beyond the Standard Model, {\it e.g.} dark matter candidates, axions, additional gauge symmetries, etc. Given this breadth, we propose that from a string phenomenology perspective, the experimental particle physics priority is the nature of the Higgs boson and the electroweak symmetry breaking mechanism. An ideal facility in the near future to study this sector is a hadron collider at 50--60 TeV that utilises contemporary magnet technology and can be built in 10-15 years from decision.

Theory of everything must include consciousness. In Part I (Vimal, 2010b) of this series of 3 articles, the subjective experience (SE) aspect of consciousness was introduced in classical physics by examining the invariance of various components of theories under PE-SE transformations, where PEs (proto-experiences) are precursors of SEs. We found that (i) classical physics is invariant under the PE-SE transformation, (ii) SEs are embedded in spacetime geometry for the structure of spacetime in superposed form, (iii) SEs can move with spatiotemporal coordinates of matter for matter field because both mental and material aspects are always together in the dual-aspect-dual-mode optimal PE-SE framework, and (iv) our specific SE is the result of matching and selection processes and can change with space and time. For example, experiencing redness has neural correlates of V4/V8/VO-red-green neural-net with redness state. When a subject moves, the specific SE redness also moves with the subject’s correlated neural-net. In the current Part II, the SE aspect of consciousness is introduced in orthodox quantum physics by examining its invariance under the PE-SE transformations. We found that the followings are invariant under the PE-SE transformations: Schrodinger equation, current, Dirac Lagrangian, the Lagrangian for a charged self-interacting scalar field, and Standard Model (the Lagrangian for free gauge field and Lagrangian for the electromagnetic interaction of a charged scalar field (Higgs Mechanism)). In Part III (Vimal, 2010c), the SE aspect of consciousness will be introduced to unify it with fundamental forces in loop quantum gravity and string theory of modern quantum physics. All parts together lead us towards the theory of everything.

Loop quantum gravity is a physical theory that aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via quantisation. General relativity describes gravity in terms of geometry; therefore, quantising such theory must be equivalent to quantising geometry and that is what loop quantum gravity does. This sounds like a mathematical task as well, thus, in this paper we will present the mathematics of loop quantum gravity. We will do it from a mathematician’s point of view. This paper is intended to be an introduction to loop quantum gravity for postgraduate students of physics and mathematics. In this work we will restrict ourselves to the three-dimensional case.