Quantum Gravity

This talk is devoted to the geometric approach to supergravity and applications in the framework of loop quantum gravity. Among other things, this approach leads to a reformulation of the theory in which (part of) supersymmetry manifests itself in terms of a gauge symmetry. Using the interpretation of supergravity in terms of a super Cartan geometry, we will derive the Holst variant of the MacDowell-Mansouri action for N=1 and N=2 AdS supergravity in D=4 for arbitrary Barbero-Immirzi parameters. We will show that these actions provide unique boundary terms that ensure local supersymmetry invariance at boundaries. The chiral case is special. The action is invariant under an enlarged gauge symmetry, and the boundary theory is a super Chern-Simons theory. The action also implies boundary conditions that link the super electric flux through, and the super curvature on, the boundary. Applications we have in mind are supersymmetric black holes and loop quantum cosmology. To this end, we will study a class of symmetry reduced models of chiral supergravity. The enlarged gauge symmetry of the chiral theory is essential as it allows for nontrivial fermionic degrees of freedom even if one imposes spatial isotropy. The quantization of the theory yields a natural state space and allows a consistent implementation of the constraint algebra.

Finally, we will give an outlook on applications towards a quantum description of supersymmetric black holes in the context of LQG and possible relations to superstring theory.

The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown that this model exhibits a symmetry under the (2+1)-dimensional Poincaré group. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. It also unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior. Remarkably, the physical ISO(2,1) symmetry can be seen as a broken infinite-dimensional symmetry. This is done by reinterpreting the action for the model as a geometric action for the BMS3 group, where the configuration space variables are elements of the algebra bms3 and the equations of motion transform as coadjoint vectors.

Zoom Link: https://pitp.zoom.us/j/99646733321?pwd=U05kYU85V0Q4VCtrZ1BNV2JZbE1DUT09

The inclusion of the cosmological constant is one of the main questions faced by quantum gravity. In three dimensions, non-perturbative approaches to quantum gravity including loop quantum gravity (LQG),  combinatorial quantization and  spinfoam path integrals encode the cosmological constant as a deformation parameter in a quantum group structure. In this talk, I will focus on the LQG approach: I will explain the Poisson-Lie structure of the classical phase space and how its quantization naturally leads to the emergence of quantum groups. I will use the holonomy-flux algebra and its spinorial presentation introduced in the series of work by Bonzom, Dupuis, Girelli, Livine and myself. This allows to construct the Hamiltonian constraint, understand its matrix elements as Turaev-Viro amplitudes. This connects LQG to the other approaches in a unified mathematical setting.

Strong gravity tests indicate that general relativity is a very accurate description of the classical dynamics of spacetime even at extreme regimes. Yet, the same dynamics can be described by "alternative" versions of general relativity such as unimodular gravity. In the quest for a quantum theory of the gravitational field, it is unclear if the quantization of such classically equivalent theories leads to the same physical predictions. In this talk, I will report on some recent results regarding this issue in the framework of continuum and perturbative quantum field theory. With a view towards ultraviolet completion, I will discuss some evidence for asymptotic safety in unimodular quantum gravity. Moreover, I will comment on the role of matter fields which couple very differently to gravity in those settings.   

Asymptotically flat spacetimes are invariant under an infinite-dimensional symmetry group comprised of superrotations and supertranslations. These symmetries are spontaneously broken, leading to an infinite degeneracy of gravitational vacua in asymptotically flat spacetimes. Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, I will describe how superrotation parametrization modes labelling distinct superrotation vacua are governed by an Alekseev–Shatashvili action on the celestial sphere. I will also comment on a recent construction of a two-dimensional effective action for the Goldstone modes of broken supertranslation invariance.

We introduce the basic elements of tensorial group field theories (TGFTs) for quantum gravity, emphasizing how they encode quantum geometry and their relation with canonical loop quantum gravity and spin foam models. Next, we discuss briefly the issue of continuum limit and how it could be understood in this framework.

In the bulk of the talk, we overview the work on the extraction of an effective cosmological dynamics from TGFTs, inspired by the idea of the universe as a quantum gravity condensate. In this context, we emphasize: the need for appropriately coarse-grained states capturing collective dynamics and the role of relational observables and their construction. We discuss what the theory says (so far) about the fate of the big bang singularity at the beginning of our universe and how it suggests a quantum gravity origin for (phantom) dark energy.

An extension of general relativity (GR) obtained by adding local quadratic terms to the action will be considered. Such theory can be a viable UV completion of GR. The additional terms soften gravity above a certain energy scale and render gravity renormalizable. The presence of 4 derivatives implies via the Ostrogradsky theorem that the classical Hamiltonian is unbounded from below. Nevertheless, I will argue that the relevant solutions are not unstable, but metastable: when the energies are much below a threshold (that is high enough to describe the whole cosmology) runaways are avoided. Remarkably, the chaotic inflation theory of initial conditions ensures that such bound is satisfied and testable implications for the early universe will be discussed. I will also argue that the basic unitarity condition is satisfied when the theory is correctly formulated at the quantum level. Moreover, thanks to the UV softening of gravity, sufficiently light objects must be horizonless and I will discuss explicit analytic examples of horizonless ultracompact objects, which have interesting physical implications.

A fundamental problem of quantum gravity is to understand the quantum evolution of black holes.  While aspects of their evolution are understood asymptotically, a more detailed description of their evolving wavefunction can be provided.  This gives a possible foundation for studying effects that unitarize this evolution, which in turn may provide important clues regarding the quantum nature of gravity.

The issue of whether quantum effects can affect gravity at cosmological distances still lacks a fundamental understanding, but there are indications of a non-trivial gravitational infrared dynamics. This possibility is appealing for building alternatives to the standard cosmological model and explaining the accelerated expansion of the Universe. In this talk I will discuss some large scale modifications of general relativity due to nonlocal terms, which are assumed to arise at the level of quantum effective action. Nonlocality is a general feature of quantum effective actions for theories with massless degrees of freedom and dynamical mass generation is a typical non-perturbative IR effect. Among several models, cosmological requirements select a single structure of the nonlocal term describing a mass for the conformal mode of the metric. The model fits very well cosmological data and has strong signatures in the tensor sector that could be tested in the future by gravitational-wave detections.

The model of Causal Dynamical Triangulations (CDT) is a background-independent and diffeomorphism-invariant approach to quantum gravity,

which provides a lattice regularization of the formal gravitational path integral. The framework does not involve any coordinate system and employs only geometric invariants. For a Universe with toroidal spatial topology, we can introduce coordinates using classical scalar fields with periodic boundary conditions with a jump. The field configurations reveal pictures of cosmic voids and filaments surprisingly similar to the ones observed in the present-day Universe. I will discuss the impact of dynamical matter fields on the geometry of a typical quantum universe in the four-dimensional CDT model and explain several observed phenomena. In particular, a phase transition is triggered by the change of the scalar field jump amplitude. This discovery may have important consequences for quantum universes with non-trivial topology since the phase transition can change the topology to a simply connected one.

In this talk I will discuss how the generators of radial conformal symmetries in Minkowski space-time are related to the generators of time evolution in conformal quantum mechanics. Within this correspondence I will show that in conformal quantum mechanics the state corresponding to the inertial vacuum for a conformally invariant field in Minkowski space-time has the structure of a thermofield double. The latter is built from a bipartite "vacuum state" corresponding to the ground state of the generators of hyperbolic time evolution, which cover only a portion of the time domain. When such generators are the ones of conformal Killing vectors mapping a causal diamond in itself and of dilations, the temperature of the thermofield double reproduces, respectively, the diamond temperature and the Milne temperature perceived by observers whose constant proper time hyper-surfaces define a hyperbolic slicing of the future cone. I will point out how this result indicates that, for conformal invariant fields, the fundamental ingredient for vacuum thermal effects in flat-space time is the non-eternal nature of the lifetime of observers rather than their acceleration.

We are experimentally investigating possible departures from the standard quantum mechanics’  predictions at the Gran Sasso underground laboratory in Italy. In particular, with radiation detectors we are searching signals predicted by the collapse models (spontaneous emission of radiation) which were proposed to solve the “measurement problem” in quantum physics and signals coming from a possible violation of the Pauli Exclusion Principle. 

I shall discuss our recent results published in Nature Physics under the title “Underground test of gravity-related wave function collapse”, where we ruled out the natural parameter-free version of the gravity-related collapse model.  I shall then present more generic results on testing CSL (Continuous Spontaneous Localization) collapse models and discuss future perspectives.

Finally, I shall briefly present the VIP experiment with which we look for possible violations of the Pauli Exclusion Principle by searching for “impossible” atomic transitions and comment the impact of this research in relation to Quantum Gravity models.