Related papers: Universal critical behavior in tensor models for f…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates five degrees of freedom; this is also verified by a new and streamlined Hamiltonian…
A new version of tetrad gravity in globally hyperbolic, asymptotically flat at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is obtained by using a new parametrization of arbitrary cotetrads to define a set of…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at…
Yang (2020a) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their analysis does not…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
We introduce and study a universal model of random geometry in two dimensions. To this end, we start from a discrete graph drawn on the sphere, which is chosen uniformly at random in a certain class of graphs with a given size $n$, for…
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with…
It has been a long entertained idea that self-bound gravitons, so-called geons, could be a dark matter candidate or form (primordial) black holes. The development of viable candidates for quantum gravity allows now to investigate these…
The four dimensional Causal Dynamical Triangulations (CDT) approach to quantum gravity is already more than ten years old theory with numerous unprecedented predictions such as non-trivial phase structure of gravitational field and…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One…
In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical…
We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume…
The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The…
In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…