Quantum Gravity

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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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