Quantum Gravity and Random Geometry

Contribution List

5. Welcome and opening remarks

1/16/23, 9:05 AM

32. Presentation of the IHP by the deputy director

Dominique Mouhanna (IHP)

1/16/23, 9:15 AM

6. The universe as a quantum fluid: quantum gravity, hydrodynamics and cosmology

Daniele Oriti (Arnold Sommerfeld Center for Theoretical Physics, LMU, Munich)

1/16/23, 9:30 AM

The hydrodynamics of quantum fluids can be mapped to relativistic cosmological dynamics, and both share the same conformal symmetries, which can be unravelled via geometric methods in superspace. This suggests a more general correspondence between hydrodynamics and cosmology, and a picture of the universe as a quantum gravity condensate. This picture is in fact realized also in some quantum...

7. Extended corner symmetry algebra and the Wald-Zoupas prescription

Simone Speziale (CNRS, CPT Marseille)

1/16/23, 10:50 AM

Boundaries and corners of gravitational subsystems allow the
construction of non-trivial Noether charges generating
infinite-dimensional symmetries, which have been advocated as a new
promising tool to understand quantum gravity. In this talk I will
focus on classical properties of these symmetries, with the goals of
explaining how they appear, how they provide a description of
non-local...

8. 3d Quantum Gravity and Quantum Groups

Maïté Dupuis

1/16/23, 11:40 AM

I will give a quick overview of the q-deformed Loop Quantum Gravity (LQG) model which describes 3-dimensional quantum gravity with a cosmological constant. The model is characterized in terms of quantum group structures and the quantum Hamiltonian constraints define the Wheeler-DeWitt equations in this framework and generate the Turaev-Viro model (with real q, q being the deformation...

9. Random matrices and magnetic amplitude for discretized strings

Thomas Krajewski (Centre de Physique Théorique, Aix-Marseille Université)

1/16/23, 2:30 PM

Magnetic amplitudes for strings in a background 3-form H involve a 2-form potential B integrated on surfaces of arbitrary topology. We propose a random matrix model whose topological expansion lead to a discretized version of these amplitudes, in the case of a propagation on an finite space X quotiented by a finite group G. Besides the fluxes induced by B, they also involve topological...

10. Towards the phase structure of first order Lorentzian Palatini gravity via Group field theory

Andreas Pithis (Universität München (LMU, ASC, MCQST))

1/16/23, 3:50 PM

The Barrett-Crane (BC) spin foam and GFT model is a state-sum model which provides a tentative quantization of first order Lorentzian Palatini gravity written as a constrained BF-theory. Its completion in terms of spacelike, timelike and lightlike components has only recently been accomplished. It is conjectured that this model gives rise to continuum spacetime with General Relativity as an...

28. Flowing from Tensor Field Theory to Tensor Models

Johannes Thürigen (WWU Münster)

1/16/23, 4:20 PM

Fields with tensor degrees of freedom provide non-trivial but tractable QFT examples. Their perturbative expansion might (but does not need to) be interpreted as generating random geometries and they can be extended to models of quantum gravity in the spirit of tensorial group field theory. In the later case the tensor degrees of freedom propagate and contribute to the scale of the theory, in...

27. Asymptotically Safe Unimodular Quantum Gravity: a Status Report

Antônio Duarte Pereira (Radboud University & Fluminense Federal University)

1/17/23, 9:30 AM

Unimodular Gravity is an alternative description of the gravitational dynamics that is equivalent to General Relativity within the classical realm. Since it is based on a different symmetry group, volume-preserving diffeomorphisms, it could be expected that Unimodular Gravity displays very different quantum properties with respect to the quantization of a full diffeomorphism-invariant theory....

13. Provable properties of asymptotic safety in f(R) approximation

Tim Morris (University of Southampton)

1/17/23, 10:50 AM

We study an $f(R)$ approximation to asymptotic safety, using a family of cutoffs, kept general to test for universality. Matching solutions on the four-dimensional sphere and hyperboloid, we prove properties of any such global fixed point solution and its eigenoperators. For this family of cutoffs, the scaling dimension at large $n$ of the $n^\text{th}$ eigenoperator, is $\lambda_n\propto b\,...

14. Entropy versus the Action in Causal Set Theory

Sumati Surya (Raman Research Institute)

1/17/23, 11:40 AM

The quantum partition function of causal set quantum gravity is a phase weighted
sum over all locally finite posets or causal sets. As the size n of the causal sets grows, however,
the overwhelmingly dominant entropic contribution comes from a class of causal sets that look nothing
like continuum spacetime. A long standing question has been whether this entropy can be overcome
in the...

15. A universal mechanism for the emergence of gravitons from effective spin foams and lattice gravity

Bianca Dittrich (Perimeter Institute)

1/17/23, 2:30 PM

Spin foams are discretized path integrals for quantum gravity based on a rigorous definition of quantum geometry. This does however lead to very complicated amplitudes, making e.g. the extraction of a continuum limit difficult. Thus, a long-standing open question was whether spin foams do describe gravity in their semi-classical and continuum limit.
The situation has changed with the recent...

30. Renormalization of composite operators in $2+\varepsilon$ quantum gravity

Riccardo Martini (INFN - Sezione di Pisa)

1/17/23, 3:50 PM

We consider higher derivative composite operators in the $\varepsilon$-expansion of 2d quantum gravity and renormalize them at one-loop. We extract the flow of the essential couplings and study their analytic continuation in the background dimensions to compare with Stelle gravity in d=4.

31. Background-independent field quantization: N-cutoffs regularization and N-geometries

Renata Ferrero (Johannes Gutenberg University Mainz)

1/17/23, 4:20 PM

We apply a novel background-independent and scale-free quantization scheme on (non-)compact maximally symmetric spacetimes. The "N-cutoffs" is a UV regularization procedure on the spectrum of the fields’ fluctuation modes implemented on the quantum number. We apply this regularization to scalar and metric fluctuations: both are found to reduce the curvature of the "N-geometries" leading to...

17. Blobbed topological recursion of the $\lambda\phi^4$ matrix model

Raimar Wulkenhaar (University of Münster)

1/18/23, 9:30 AM

We consider an $N\times N$ Hermitian matrix model with measure $d\mu_{E,\lambda}(\Phi)=\frac{1}{Z} \exp(-\frac{\lambda N}{4} \mathrm{tr}(\Phi^4)) d\mu_{E,0}(\Phi)$ where $d\mu_{E,0}$ is the Gau\ss{}ian measure with covariance $\langle \Phi_{kl}\Phi_{mn}\rangle =\frac{\delta_{kn}\delta_{lm}}{N(E_k+E_l)}$ for given $E_1,...,E_N>0$. We explain how this setting gives rise to two ramified coverings...

20. Topological recursion for weighted Hurwitz numbers

Valentin Bonzom (LIPN - Institut Galilée - Université Paris 13)

1/18/23, 10:50 AM

Combinatorial maps are a well-known discrete approach to 2-dimensional quantum gravity. Planar maps satisfy multiple universal properties at large scale, which guarantee the universality of the continuum limit. But more universal structures can be observed in the all-genera structures of maps, e.g. they satisfy the KP integrable hierarchy and the topological recursion. Double weighted Hurwitz...

23. Topological recursion in 2d quantum gravity

Gaetan Borot (Humboldt-Universität zu Berlin)

1/18/23, 11:40 AM

I will explain the idea of topological recursion, its implementation for the enumeration of maps (and of large maps), and mention other applications to compute integrals over the moduli space of Riemann surfaces M_{g,n}. I will introduce the idea of geometric recursion which in certain cases allows for a fully geometric proof that topological recursion solves such problems.

26. A combinatorial approach to random hyperbolic surfaces

Timothy Budd (Radboud University, Nijmegen, The Netherlands)

1/19/23, 9:30 AM

Starting with dynamical triangulations of the string world sheet and matrix models, random maps have occupied a central place in the study of 2d (Euclidean) quantum gravity. Advances in combinatorics (e.g. tree bijections) and probability theory (e.g. Gromov-Hausdorff limits of random metric spaces) led to a rigorous construction of 2d quantum gravity in the form of Brownian geometry on...

21. Does GCDT solve the Hubble constant tension ?

Jan Ambjorn

1/19/23, 10:50 AM

CDT might define a quantum theory of gravity, but how one can locate the asymptotic safety UV fixed point is still unclear. However, so-called  generalized CDT models, which allow for baby universe creation, make it possible to conjecture how quantum corrections can influence late time cosmology. The quantum corrections lead to a modified Friedmann equation which does not involve a...

24. Graviton, boundaries, BMS symmetry and its cocycles and Beltrami parametrization

Laurent Baulieu (LPTHE)

1/19/23, 11:40 AM

Done in collaboration with Tom Wetzstein

18. Perturbing isoradial triangulations

Francois David

1/19/23, 2:30 PM

Isoradial triangulations are example of critical planar graphs, on which discrete analyticity, integrability, discrete and continuous conformal invariance can be defined and studied for many models. I present some results on the deformations of such triangulations, which break integrability, and their effect on the critical Laplacian and some of its extensions, and for their conformal...

11. Trisections in colored tensor models

Reiko Toriumi (OIST)

1/19/23, 3:50 PM

We give a procedure to construct trisections for closed $4$-manifolds generated by colored tensor models without restrictions on the number of simplices in the triangulation, therefore generalizing previous works in the context of crystallizations and PL-manifolds. We give a description of how trisection diagrams can arise from colored tensor model graphs for closed $4$-manifolds.

29. Generalised spectral dimensions in non-perturbative quantum gravity

Marcus Reitz (Jagiellonian University)

1/19/23, 4:20 PM

The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. This scale-dependent effective dimension in quantum gravity has been found by studying the propagation of scalar fields. It is however possible that the non-manifold like structures, that are...

19. Emergence of macroscopic spacetimes in a certain large-N limit of canonical tensor model

Naoki Sasakura (Yukawa Institute for Theoretical Physics, Kyoto University)

1/20/23, 9:30 AM

It is challenging to realize emergence of macroscopic spacetimes in tensor models. We study a wave function of a tensor model in the canonical formalism in a certain large-N limit, in which the wave function can reliably be computed classically (namely, by saddle points). We show that spacetimes develop through successive first-order phase transitions, in which numbers of “points” increase one...

22. Ubiquity of melonic limits in tensor models

Sylvain Carrozza (Radboud University)

1/20/23, 10:50 AM

Analogously to matrix models, which provide a combinatorial approach to two-dimensional quantum gravity, tensor models appear to be well-suited to investigations of random geometry in higher dimensions. Indeed, certain generating functions of discrete (pseudo)manifolds, of arbitrary but fixed dimension, can be expressed in terms of (formal) tensor integrals. This being said, obtaining...

25. Higher gauge and discrete geometry

Florian Girelli

1/20/23, 11:40 AM

Crossed modules, or (strict) 2-groups, can be used to decorate faces and edges of a 2-complex. In this sense they provide a generalization of lattice gauge theory. I will discuss how these structures are relevant to 4d topological models, possibly to 4d quantum gravity and also provide new mathematical symmetry structures to explore.

12. tba

Petr Horava (University of California, Berkeley)