Quantum Gravity

I’ll give a review of extended phase space in gauge theories and/or diffeomorphism-invariant theories, beginning with its original conception up to our most recent work. The primary focus in a classical theory is on the proper representation of symmetries and gauge symmetries on phase space. Correspondingly, this is understood in the quantum theory through the crossed product construction and conditional expectation. I’ll discuss several examples.

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Incorporating time poses a challenge for all quantum gravity programs primarily build around Euclidean spacetimes. This talk surveys how the gravitational asymptotic safety program may address this challenge by encoding the gravitational degrees of freedom via the Arnowitt-Deser-Misner (ADM) decomposition of the spacetime metric. This formulation equips spacetime with a foliation structure singling out a preferred direction. This structure may then take the role of time in the Lorentzian framework. Within this setting, we will outline recent results related to the Wilsonian renormalization group flow of the graviton two-point function including the infrared attractors rendering the graviton massless. Furthermore, we will explain how these results generalize to Lorentzian signature spacetimes and briefly comment on potential applications in the context of cosmology.

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Zoom link https://pitp.zoom.us/j/98382991491?pwd=SmtpMTRTK2NUMEpuN3laa0pIWWs2UT09

Group field theory (GFT) is a background independent approach to quantum gravity in which the quanta represent "building blocks of space". It has been successfully applied to the cosmological setting and shown to have the potential for rich phenomenology. In this talk we will explore a novel proposal to construct operators in GFT based on symmetries of the action, which can then be identified with respective classically conserved currents. This construction relies on a relational coordinate system spanned by four massless scalar fields. As the classical currents are related to the components of the metric, the expectation values of the new GFT operators can be interpreted as giving rise to an effective metric originating directly from the quantum theory. We proceed to investigate the implications of this proposition for a flat homogeneous universe and its perturbations.

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Zoom link https://pitp.zoom.us/j/98843634192?pwd=OWs1SEdiWnIyYmlSbTh3bU9MaDBDdz09

It is a general expectation in several approaches to quantum gravity that continuum physics emerges as a macroscopic phenomenon from the collective behavior of fundamental quantum gravity degrees of freedom. However, a physical understanding of this emergence process requires us to address deeply intertwined technical and conceptual issues. In this talk, I will focus on two of them: the localization problem, related to the background independence of the underlying quantum gravity theory, and the coarse-graining problem, related to the extraction of the macroscopic, continuum physics from the microscopic, quantum-gravitational one. After discussing what strategies can be adopted in general to address these issues, I will show a concrete implementation of such strategies in the context of the group field theory approach to quantum gravity. I will then demonstrate how these strategies can be employed to extract cosmological physics from group field theories, allowing to clarify the intrinsically quantum-gravitational nature of cosmic structures and to characterize the impact of quantum gravity effects on the emergent cosmological dynamics.

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Zoom link https://pitp.zoom.us/j/99070866809?pwd=Y1VGdGR5clZ0bTFwY2dBRHBwU3ptUT09

In this presentation, I will discuss two distinct topics, one relating to the foundational aspects of LQG and the other concerning its applicational implications.
Firstly, I will explore the U(1)^3 model of Euclidean Quantum Gravity, which serves as an interesting testing ground for the dynamics problem in LQG. With its analogous constraint structure to full gravity, the U(1)^3 model may hold the key to enhanced quantization techniques.

Secondly, I will delve into the asymptotic symmetries of General Relativity in the Ashtekar-Barbero formulation. New parity conditions for the Ashtekar-Barbero variables will be proposed, which do produce non-trivial supertranslation charges at spatial infinity. This development paves the way for investigating the quantum characteristics of supertranslation charges within the context of LQG.

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Zoom link https://pitp.zoom.us/j/99532986538?pwd=cnU0VnpJbjU4TSt4MEEzVngxb2wvdz09

According to the Belinski-Khalatnikov-Lifshitz conjecture, the Bianchi IX spacetime describes the evolution of each spatial point close to a generic spacelike singularity. However, near the singularity, quantum effects are expected to be relevant. Therefore, in this work a quantum analysis of the model is performed, mainly focusing on its chaotic nature. Considering some minimal approximations, it is possible to encode all the information of the quantum degrees of freedom in certain canonical variables, expanding thus the classical phase space. In this way, we can apply the usual methods of dynamical systems for studying chaos. In particular, two techniques are considered. On the one hand, an analytical study is carried out, which provides an isomorphism between the quantum dynamics of Bianchi IX and the geodesic flow on a Riemannian manifold. On the other hand, by means of numerical simulations, the fractal dimension of the boundary between points with different outcome in the space of initial data is studied. The main conclusion is that, although the quantum system is chaotic, the quantum effects considerably reduce this behavior as compared to its classical counterpart.

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Zoom link https://pitp.zoom.us/j/91559466008?pwd=UzQvTGRkR3VQWm9MWDlaaVAyNi9EQT09

In the quest to understand the fundamental structure of spacetime (and subsystems) in quantum gravity, it may be worth exploring the ultimate consequences of non-perturbative canonical quantization, carefully taking into account the constraints and gauge invariance of general relativity. As the reduced phase space (or even the pre-phase space) of gravity lacks a natural linear structure, a generalization of the standard method of quantization (based on global conjugate coordinates) is required. One such generalization is Isham's method based on transitive groups of symplectomorphisms, which we test in some simple examples. In particular, considering a particle that lives on a sphere, in the presence of a magnetic monopole flux, we algebraically recover Dirac's charge quantization condition from a "Casimir matching principle", which we propose as an important tool in selecting natural representations. Finally, we develop the non-perturbative reduced phase space quantization of causal diamonds in (2+1)-dimensional gravity. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$. Applying Isham's quantization we find that the Hilbert space of the associated quantum theory carries a (projective) irreducible unitary representation of the $BMS_3$ group. From the Casimir matching principle, we show that the states are realized as wavefunctions on the configuration space with internal indices in unitary irreps of $SL(2, \mathbb{R})$. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the boundary length.

Papers on quantization of causal diamonds:
https://arxiv.org/abs/2308.11741
https://arxiv.org/abs/2310.03100

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Zoom link https://pitp.zoom.us/j/98636934234?pwd=THBCcFpYWHYzWmY0YjViY3Q1a3VYdz09

Recently, models with different properties have been proposed for polymerized dust collapse and regular black holes. To fully understand their properties and differences, we provide a systematic procedure to construct effective polymerized spherically symmetric models encoding holonomy corrections as $1+1$d field theory from effective regular cosmological dynamics or stationary effective metrics. We apply this formalism and consider models that have the following advantages: The effective dynamics can be derived from a class of extended mimetic gravity Lagrangians in 4 dimensions. The models admit a consistent Lemaitre-Tolman-Bondi (LTB) condition, by which the dynamics is completely decoupled along the radial direction in LTB coordinates, trivializing the junction condition in dust collapse. The class of effective dynamics admits a polymerized Birkhoff-like theorem, which leads to a stationary effective metric in the polymerized vacuum. The effective dynamics can reproduce known regular black hole solutions, including Bardeen and Hayward, by a suitable choice of holonomy corrections. As a concrete example, we construct an effective model compatible with the improved dynamics of loop quantum cosmology in the decoupled LTB sector. We compare it with several effective polymerized models recently introduced in the context of loop quantum gravity and gain some new insights into the presence of shocks.

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Zoom link https://pitp.zoom.us/j/99966795418?pwd=Ty9mRXNML3NsUXdvcU1WUTdCaWpVZz09

Abstract TBA

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Zoom link https://pitp.zoom.us/j/92901106970?pwd=SEdZajRQYWlrQzJhRnM0WnRpeHVNdz09

In the last years, asymptotic symmetries have regained a lot of interest, and various extensions of the well known BMS group have been considered in the literature. Many charges associated to the diffeomorphisms of the sphere (superboosts and superrotations) have been proposed, but it has not been clear if these charges can be derived from a symplectic potential that is covariant and stationary, i.e satisfying the Wald-Zoupas usual requirements. In this talk I will consider a new asymptotic symmetry group, which is a one dimensional extension of the generalized-BMS group, and construct a stationary symplectic potential, covariant with respect to these symmetries, by adding corner terms to the usual Einstein-Hilbert symplectic potential. Then, we will recover the charges introduced by Compère, Fiorucci and Ruzziconi for superboosts and superrotations. In order to ensure covariance, we will need to introduce an edge mode which has already appeared in the literature, the supertranslation field. I will also explain that its introduction as a corner term can lead us to construct a local (asymptotic) notion of energy for the gravitational waves, providing a physical interpretation of the new charges.

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Zoom link https://pitp.zoom.us/j/97926664729?pwd=VzV2VmQ4eVlzcFdaZkNBNnpqRkMvUT09

To develop a quantum gravity theory, it is fundamental to move away from the gauge-fixing approach and instead employ a gauge-free analysis. There is an increasing body of evidence suggesting that the symmetries employed for gauge-fixing might carry charge. Consequently, setting the associated fields to zero is a physical constraint on the system, which should be avoided. In this talk, we will examine a partial fixing of the Fefferman-Graham (FG) gauge, referred to as the Weyl-Fefferman-Graham (WFG) gauge, which restores boundary Weyl covariance. We will show that the diffeomorphism mapping WFG to FG can be charged and discuss how this relates to holography.

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Zoom link https://pitp.zoom.us/j/93359035909?pwd=aHo0TUFXekZaeCtrT2FzNDZKUW15Zz09

We use a result of Hawking and Gilkey to define a Euclidean path integral of gravity and matter which has the special property of being independent of the choice of basis in the space of fields. This property allows the path integral to describe also physical regimes that do not admit position bases. These physical regimes are pre-geometric in the sense that they do not admit a mathematical representation of the physical degrees of freedom in terms of fields that live on a spacetime. In regimes in which a spacetime representation does emerge, the geometric properties of the emergent spacetime, such as its dimension and volume, depend on the balance of fermionic pressure and bosonic and gravitational pull. That balance depends, at any given energy scale, on the number of bosonic and fermionic species that contribute, which in turn depends on their masses. This yields an explicit mechanism by which the effective spacetime dimension can depend on the energy scale.

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Zoom link https://pitp.zoom.us/j/91471624951?pwd=RDBYTXc2MGs5bkFKUytYR0huOHYwdz09