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...

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...

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...

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...

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...

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....

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\,...

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...

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...

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.

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...

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...

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...

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.

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...

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...

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...

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...