相关论文: On the behavior of extreme $d$-dimensional spatial…

Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…

We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…

The theory of massive gravity possesses ambiguities when the spacetime metric evolves far from the non-dynamical fiducial metric used to define it. We explicitly construct a spherically symmetric example case where the metric evolves to a…

We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups…

The possible interpretations of a new continuum model for the two-dimensional quantum gravity for $d>1$ ($d$=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we…

Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and $T-$linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead…

This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature…

It is widely believed and in part established that exact global symmetries are inconsistent with quantum gravity. One then expects that approximate global symmetries can be quantitatively constrained by quantum gravity or swampland…

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters…

We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…

We study existence and nonexistence of diagonal and separating coordinates for Riemannian symmetric spaces of rank 1. We generalize the results of Gauduchon and Moroianu, 2020, by showing that a symmetric space of rank 1 has diagonal…

Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction…

Most astrophysical systems in our Universe are characterized by shallow gravitational potentials, with dimensionless compactness $|\Phi| \equiv r_s / R \ll 1$, where $r_{s}$ and $R$ are their Schwarzschild radius and typical size,…

The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…

We construct cubic gravity and its $f(P)$ extension and we investigate their early- and late-time cosmological applications. Cubic gravity is based on a particular invariant $P$, constructed from cubic contractions of the Riemann tensor,…

Let $(X,d)$ be a finite ultrametric space. In 1961 E.C. Gomory and T.C. Hu proved the inequality $|Sp(X)|\leqslant |X|$ where $Sp(X)=\{d(x,y)\colon x,y \in X\}$. Using weighted Hamiltonian cycles and weighted Hamiltonian paths we give new…

We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which…

Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of…

Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…

The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection…