Related papers: Towards background independent quantum gravity wit…
In the tensorial group field theory (TGFT) approach to quantum gravity, the basic quanta of the theory correspond to discrete building blocks of geometry. It is expected that their collective dynamics gives rise to continuum spacetime at a…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
We review an approach which aims at studying discrete (pseudo-)manifolds in dimension $d\geq 2$ and called random tensor models. More specifically, we insist on generalizing the two-dimensional notion of $p$-angulations to higher…
The metric-affine gravity provides a useful framework for analyzing gravitational dynamics since it treats metric tensor and affine connection as fundamentally independent variables. In this work, we show that, a metric-affine gravity…
Perturbing the standard Gross-Neveu model for $N^3$ fermions by quartic interactions with the appropriate tensorial contraction patterns, we reduce the original $U(N^3)$ symmetry to either $U(N)\times U(N^2)$ or $U(N)\times U(N)\times…
We show that the phase space of three-dimensional gravity contains two layers of dualities: between diffeomorphisms and a notion of "dual diffeomorphisms" on the one hand, and between first order curvature and torsion on the other hand.…
We introduce a pregeometry employing uniform spaces over the denumerable set X of spacetime events. The discrete uniformity D_X over X is used to obtain a pregeometric model of macroscopic spacetime neighborhoods. We then use a uniformity…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
For some theories where the degrees of freedom are tensors of rank $3$ or higher, there exist solvable large $N$ limits dominated by the melonic diagrams. Simple examples are provided by models containing one rank-$3$ tensor in the…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional…
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of…
This is the first of a series of papers dedicated to the study of the partition function of three-dimensional quantum gravity on the twisted solid torus with the aim to deepen our understanding of holographic dualities from a…
We explore the influence of geometry in the critical behavior of sparse long-range spin models. We examine a model with interactions that can be continuously tuned to induce distinct changes in the metric, topology, and dimensionality of…
We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and…
In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition…
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the…
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However,…
In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition.…