Quantum Gravity

Correlation functions are ubiquitous in quantum field theory, but their use in quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties with diffeomorphism invariance and the dynamical nature of geometry. We address these challenges in the context of nonperturbative quantum gravity, motivated by the goal of computing geometric correlators from first principles, as a possible window to early-universe cosmology. I will report on recent work in 2D Lorentzian quantum gravity, formulated in terms of causal dynamical triangulations, which demonstrates the feasibility of constructing and measuring manifestly diffeomorphism-invariant curvature correlators. I will discuss some unusual features of the connected correlators and new results on their behaviour in two dimensions, obtained with the help of Monte Carlo simulations.

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At the classical level, one can restrict a spherically symmetric model to the corresponding LTB sector by requiring that a so-called LTB condition is satisfied. In this talk we will discuss how this can be generalised in the context of effective models containing quantum gravity inspired modifications of  the classical theory in the form of polymerisations. The formalism presented allows us to consider more general polymerisations than in previous work in the literature. Applications of this framework are then considered, focusing on a particular class of models that have the property that the effective dynamics is completely decoupled along the radial direction. Examples of effective models that fall into this class are discussed and their physical properties are compared with existing models in the literature.

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I will review recent progress in the asymptotic safety approach to quantum gravity. This includes the computation of momentum-dependent graviton correlation functions, the structure of the Standard Model with asymptotically safe gravity, and the recent first computation directly in space-times with Lorentzian signatures via the spectral function of the graviton. Overall, I will display the progress towards the computation of the quantum effective action which encapsulates effective field theory in the IR limit and the asymptotic safety regime in the UV limit.

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We show that the Ryu-Takayanagi (RT) formula, originally introduced to compute the entropy of a holographic boundary CFT, can be interpreted as entropy of an algebra of bulk gravitational observables. In particular, we show that any Euclidean gravitational path integral satisfying a simple and familiar set of axioms defines type I von Neumann algebras of bulk observables acting on closed codimension-2 asymptotic boundaries. The entropies associated to these algebras, defined via the gravitational path integral, can be written in terms of standard density matrices and standard Hilbert space traces, and in appropriate semiclassical limits are computed by the RT formula with quantum corrections. Our work thus provides a bulk state-counting interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, they may be expected to hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

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Extended BMS symmetry is believed to be a fundamental symmetry of any classical gravitational scattering process, as well as of the quantum gravity S-matrix. We explore this property using the BRST formulation of BMS symmetry, which allows to construct a non trivial solution of the Wess-Zumino consistency condition at the null boundaries of spacetime. We interpret this solution as an anomaly for asymptotic BRST Ward identities for superrotations. By relating them to the leading and subleading soft graviton theorem, we recover the well known results that the leading soft theorem is exact at all loop in perturbation theory without ever referring to Feynman diagrams, while the anomaly for superrotations is at the origin of the 1-loop correction to the subleading soft factor. This construction provides a rigorous, fully quantum origin for the invariance of the S-matrix under asymptotic symmetries.

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When the spacetime metric is regarded as a quantum field, the classical trajectories of freely falling objects are subject to random fluctuations, or “noise”. This fundamental noise might even be observable at gravitational wave detectors: if detected, it would provide experimental evidence for the quantization of gravity. The effect of the quantum-gravitational noise is to turn the classical geodesic deviation equation into a stochastic, Langevin-like equation. Moreover, when these results are extended to congruences of geodesics, the quantum fluctuations of spacetime give rise to an additional term in the Raychaudhuri equation with the same sign as the other terms.

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We explore the physical consequences of embedding Einstein gravity with negative cosmological constant in Conformal Gravity in four dimensions. In the bulk, the procedure is equivalent to Holographic Renormalization, as the Einstein-AdS action appears augmented by the correct boundary counterterms. In codimension-2, 4D Conformal Gravity induces a 2D conformal invariant, which leads to a renormalized area for minimal surfaces attached to the conformal boundary. For arbitrary surfaces, this proposal reproduces other energy functionals as Willmore Energy and Reduced Hawking Mass. In particular, this procedure provides a more geometric approach to the computation of Holographic Entanglement Entropy for CFTs dual to 4D Einstein gravity.

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We tackle the question of whether regular black holes or other alternatives to the Schwarzschild solution can arise from an action principle in quantum gravity. Focusing on an asymptotic expansion of such solutions and inspecting the corresponding field equations, we demonstrate that their realization within a principle of stationary action would require either fine-tuning, or strong infrared non-localities in the gravitational effective action. We will also show that the black hole entropy of theories displaying such infrared non-localities diverge. The principle of least action and the consistency of Wald entropy thus yield non-trivial asymptotic constraints on the metric of quantum black holes.

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I present work done in the last years on the construction of dynamical coordinate systems for highly symmetric backgrounds, such as Minkowski, de Sitter, and FLRW cosmologies, and which are needed in the relational approach to construct gauge-invariant observables in gravity. I show that it is possible to restrict the inevitable non-local contributions to the past light cone such that the obtained observables are causal. Lastly, I present some applications, namely the leading quantum gravitational corrections to the local expansion rate of our universe (the Hubble rate) and the Newtonian gravitational potential.

Based on arXiv:1711.08470, arXiv:1806.11124, arXiv:2108.11960, arXiv:2109.09753, and arXiv:2303.16218.

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Horizons of black holes in equilibrium and null infinity of asymptotically flat space-times are null 3-manifolds but have very different physical connotations. We first show that they share a large number of geometric properties, making them both weakly isolated horizons. We then use this new unified perspective to unravel the origin of the drastic differences in the physics they contain. Interestingly, the themes are woven together in a manner reminiscent of voices in a fugue.The talk is based on joint work with Simone Speziale (arXiv:2401.15618 and arXiv 2401:????).

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In my talk I will review motivation for and construction of an infinite derivative gravity. Especially a connection to the string field theory will be highlighted. Then I will demonstrate an exact embedding of the Starobinsky inflation in this construction. In final part I will speak about modifications to observable compared to local models of inflation: spectral indexes, tensor/to scalar ratio, shapes of non-gaussianities and related parameters, gravitational waves production.

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Carrollian holography aims to express gravity in asymptotically flat space-time in terms of a dual Carrollian CFT living at null infinity. In this talk, I will review some aspects of Carrollian holography and argue that this approach is naturally related to the AdS/CFT correspondence via a flat limit procedure. I will then introduce the notion of Carrollian amplitude, which allows to encode massless scattering amplitudes into boundary correlators, and explain its connection to celestial amplitudes. Finally, I will present recent results concerning Carrollian OPEs and deduce how soft symmetries act at null infinity.

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