Quantum Gravity

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.

 

Asymptotically safe gravity is one of the most conservative approaches to quantum gravity. It relies on the framework of quantum field theory and the Wilsonian renormalization group. Recently, questions and open issues have been discussed both within and outside its community. This week, instead of a seminar, we will have a debate between John Donoghue ("A Critique of the Asymptotic Safety Program", arXiv:1911.02967) and Roberto Percacci ("Critical reflections on asymptotically safe gravity", arXiv:2004.06810), who will critically discuss the status of the field, and highlight its strengths and challenges. 

Across different scales, symmetries shape physical systems: for example, in effective theories in condensed matter, various global symmetries are realized; at higher energy scales, the local symmetries of the Standard Model of particle physics take over. But what is the fate of symmetries at the Planck scale, where quantum gravity fluctuations kick in?

In this talk, I will focus on this question mainly from the perspective of asymptotic safety and will highlight a number of results about the role of symmetries in the interplay of asymptotically safe quantum gravity with matter. I will then mainly focus on particular discrete global symmetries, which have the attractive feature of generating mass-hierarchies without extra fine-tuning, and discuss whether or not these could be realized in quantum-gravity-matter models.

The Hartle-Hawking-Vilenkin state is defined on mini-superspace and is semiclassically related to inflationary theory.  However, the state suffers a few problems connected to the path integral of Euclidean or the Lorentzian measure of metrics.  In this talk, we will explore a way around these issues by working in the (Ashtekar) connection representation, a real Kodama-Chern-Simons state.  We find a generalized "Fourier Transform" that related the Chern-Simons-Kodama state to the Hartle-Hawking state beyond mini-superspace.  We end with some discussion and open ended questions for cosmology and quantum gravity.

I will consider the phase space at null-infinity from the r\rightarrow\infty limit of a quasi-local phase space for a finite box with a boundary that is null. This box will serve as a natural IR regulator. To remove the IR regulator, I will consider a double null foliation together with an adapted Newman--Penrose null tetrad. The limit to null infinity (on phase space) is obtained in the limit where the boundary is sent to infinity. I will introduce various charges and explain the role of the corresponding balance laws. The talk is based on the paper: arXiv:2012.01889.

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.