Quantum Gravity

A remarkable aspect of 4-dimensional complexified General Relativity (GR) is that it can be non-trivially deformed: there exists an infinite-parameter set of modifications with the same degree of freedom count. It is trivial to impose reality conditions that lead to real theories with Euclidean or split signature, but the situation is more complicated and not yet fully understood in the Lorentzian case, which is the subject of this talk. I will first show that the choice of potentially consistent reality conditions is essentially unique and boils down to the reality of the underlying 3-metric at the canonical level, as in the case of GR. For simplicity, I will focus on a subset of modified theories that correspond to a natural extension of Ashtekar's Hamiltonian constraint, namely, a linear combination of EEE, EEB, EBB and BBB. Interestingly, the evolution equations for the 3-metric and its first time-derivative take the same form as in GR, but with an effective stress tensor source which cannot be expressed in terms of these two fields. Modified theories therefore appear as essentially "non-metric" in that they do not admit a closed geometrodynamics form. In particular, this obstructs the conservation of the reality conditions, because the effective source remains complex. Alternatively, if we insist on reality, we obtain extra reality conditions which then leave no room for degrees of freedom. I will finally argue that this should be a generic feature of the Lorenzian modified theories, in stark contrast to their Euclidean and split-signature counterparts.

I describe the non-relativistic c→∞ and ultra-relativistic c→0 limits of the kappa-deformed symmetries, with and without a cosmological constant.  The corresponding kappa-Newtonian and kappa-Carrollian noncommutative spacetimes are also obtained. These constructions show the non-trivial interplay between the quantum deformation parameter kappa, the curvature parameter Lambda and the speed of light parameter c.

There are three distinct regions where quantum gravity becomes non-negligible in a black hole spacetime.  There is a precise sense in which these three regions are causally disconnected, and therefore arguably independent.   I illustrate a number of indications we have about what happens in each of them, coming both from the classical Einstein equations and from loop quantum gravity.  These point all to an interesting scenario: long living remnants stabilized by quantum gravity, formed by a large and slowly decreasing interior enclosed into a small anti-trapping horizon. Contrary to what too often stated, the scenario offers also a proof of principle that there is no tension between unitarity and the equivalence principle: the tension comes from postulating a version of holography which is too strong: a fad, for which there is no solid physical evidence.

The melonic limit of a field theory is a large-N limit in which melonic diagrams dominate, thus differing significantly from the cactus and planar limits of vector and matrix models. It was first discovered in tensor models in zero dimensions, viewed as an approach to quantum gravity, and later in the SYK model. More recently, it has found applications in quantum field theory on a fixed (flat) background as an analytic tool for the study of new fixed points of the renormalization group, i.e. new conformal field theories. In this talk, I will review the main features of the melonic limit, and in view of the recent developments I will revisit an old model by Amit and Roginsky with SO(3) internal symmetry, which is neither a tensor model nor a disordered model like SYK, and yet it has a similar melonic limit. Time permitting, I will also comment on similarities with the fishnet model by Kazakov et al, and on the (in)stability of all such models when complex scaling dimensions appear.

The Principle of Equivalence, stating that all laws of physics take their special-relativistic form in any local inertial frame, lies at the core of General Relativity. Because of its fundamental status, this principle could be a very powerful guide in formulating physical laws at regimes where both gravitational and quantum effects are relevant. However, its formulation implicitly presupposes that reference frames are abstracted from classical systems (rods and clocks) and that the spacetime background is well defined. Here, we we generalise the Einstein Equivalence Principle to quantum reference frames (QRFs) and to superpositions of spacetimes. We build a unitary transformation to the QRF of a quantum system in curved spacetime, and in a superposition thereof. In both cases, a QRF can be found such that the metric looks locally flat. Hence, one cannot distinguish, with a local measurement, if the spacetime is flat or curved, or in a superposition of such spacetimes. This transformation identifies a Quantum Local Inertial Frame. These results extend the Principle of Equivalence to QRFs in a superposition of gravitational fields. Verifying this principle may pave a fruitful path to establishing solid conceptual grounds for a future theory of quantum gravity.

Euclidean quantum gravity approaches have a long history but suffer from a number of severe issues.  This gives a strong motivation to develop Lorentzian approaches. Spin foams constitute an important such approach, which incorporate a rigorously derived discrete area spectrum.  I will explain how this discrete area spectrum is connected to the appearance of an anomaly, which explains the significance of the Barbero-Immirzi parameter and forces an extension of the quantum configuration space, to also include torsion degrees of freedom. This can be understood as a defining characteristic of the spin foam approach, and provides a pathway to an (experimental) falsification.

All these features are captured in the recently constructive effective spin foam model, which is much more amenable to numerical calculations than previous models.  I will present numerical results that a) show that spin foams do impose the correct equations of motion b) highlight the influence of the anomaly and c) underline the difference to Euclidean quantum gravity.  I will close with an outlook on the features that can be studied with a truly Lorentzian model, e.g. topology change.

I will review the analysis of boundary symmetries in first order 3d gravity, and explain how the study of the boundary current algebra and the Sugawara construction actually leads to two dual notions of diffeomorphism charges. This provides a new understanding of the relationship between the second order and first order formulations, and of the existence of finite distance asymptotic symmetries (as strange as this sounds) in topological theories. This analysis is performed on the most general theory of first order 3d gravity, which also enables to understand the duality between curvature and torsion, as well as the relationship with chiral and massive gravity.

If time is described by a fundamental process rather than a coordinate, it

interacts with any physical system that evolves in time. The resulting
dynamics has recently been shown to be consistent provided the fundamental
period of the time system is sufficiently small. A strong upper bound T_C
< 10^{-33}s of the fundamental period of time, several orders of magnitude
below any direct time measurement, can be obtained from bounds on
dynamical variations of the period of a lab system evolving in time.
Possible cosmological implications will be discussed.

In this seminar, I will consider a deformed kinematics that goes beyond special relativity as a way to account for possible low-energy effects of a quantum gravity theory that could lead to some experimental evidences. This can be done while keeping a relativity principle, an approach which is usually known as doubly (or deformed) special relativity. In this context, I will give a simple geometric interpretation of the deformed kinematics and explain how it can be related to a metric in maximally symmetric curved momentum space. Moreover, this metric can be extended to the whole phase space, leading to a notion of spacetime. Also, this geometrical formalism can be generalized in order to take into account a space-time curvature, leading to a momentum deformation of general relativity. I will explain theoretical aspects and possible phenomenological consequences of such deformation.

The quantum states of matter in the immediate vicinity of a black hole can be studied using no other information than Standard Model physics combined with perturbative gravity. The point is that the relevant energy scale of the most important fields involved is low compared to the Planck scale, provided the black hole is big compared to the Planck scale. Usually this problem is investigated by using the metric that includes the effects of matter that formed the black hole in the distant past and sometimes also matter that is radiated away in the distant future.  Arguments are presented however to justify that one should ignore those effects. The metric then becomes invariant under  time translation, and this is what we need to get the energy eigen states. It is this scheme that forces us to impose the antipodal identification as a new boundary condition, giving us a beautiful picture of black hole quantum evolution. The logic of choosing this compulsory topological twist in space-time is explained. There are still many very hard questions and I hope to be able to inspire people to look into these.

I will discuss challenges of quantum gravity, highlighting conceptual, methodological as well as phenomenological aspects. Focusing on asymptotically safe quantum gravity, I will review recent progress in addressing key theoretical challenges using continuum and lattice methods. Furthermore, I will explain how the high predictive power of the asymptotically safe fixed point for quantum gravity and matter might allow us to explain fundamental properties of our universe, for example its dimensionality. Finally, I will point out possible connections between different approaches to quantum gravity, and how these connections might help us formulating a fundamental description of nature.

I will show that quasinormal modes of black holes could be used to investigate quantum gravity or modified gravity in specific situations. Some general comments about isospectrality will also be made. Finally a few other quantum gravity phenomena associated with black holes will be underlined.