相关论文: Gaussian Free Fields and KPZ Relation in R^4

Using a stochastic control approach we establish couplings of the Liouville field and the sinh-Gordon field with the Gaussian free field in dimension $d=2$, such that the difference is in a Sobolev space of regularity $\alpha>1$. The…

We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the…

We construct measures on the space $\mathcal D'(Q_p^n)$, $n\le 4$, of Bruhat-Schwartz distributions over the field of $p$-adic numbers, corresponding to finite volume polynomial interactions in a $p$-adic analog of the Euclidean quantum…

The so called "New Massive Gravity" in $D=2+1$ consists of the Einstein-Hilbert action (with minus sign) plus a quadratic term in curvatures ($K$-term). Here we perform the Kaluza-Klein dimensional reduction of the linearized $K$-term to…

We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems. The tensor-product structure allows us to derive density matrices and Born's rule for $d=2$…

To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum…

We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat…

As it is known, Gleason's theorem is not applicable for a two-dimensional Hilbert space since in this situation Gleason's axioms are not strong enough to imply Born's rule thus leaving room for a dispersion-free probability measure i.e.,…

The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the…

We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two point correlation function of the sine-Gordon theory is…

We apply the general theory of Cauchy biorthogonal polynomials developed previously by the authors, to the case associated with Laguerre measures. In particular, we obtain explicit formulae in terms of Meijer-G functions for all key objects…

A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…

In this PhD Thesis we investigate the geometry of random fields on compact Riemannian manifolds, in particular the two-dimensional sphere. In the first part, we characterize isotropic Gaussian fields on homogeneous spaces of a compact group…

In this paper, we investigate the entropy of the free gravitational field for a given epoch for some well-known isotropic and anisotropic cosmologies. We use the definition of gravitational entropy proposed by Clifton, Ellis, and Tavakol,…

f(T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenb\"{o}ck connection. This connection describes a spacetime with zero curvature but with…

We seek for an alternative to the metric tensor $g_{\mu\nu}$ as a fundamental geometrical object in four-dimensional Riemannian manifolds. We suggest that the metric tensor $g_{\mu\nu}(P)$ at a given point $P$ of a manifold may be replaced…

The free (4,0) superconformal theory in 6 dimensions and its toroidal dimensional reductions are studied. The reduction to four dimensions on a 2-torus has an $SL(2,\Z)$ duality symmetry that acts non-trivially on the linearised gravity…

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…

We investigate the relation between 3d N=2 theories and 2d free field correlators or Dotsenko-Fateev (DF) integrals for Liouville CFT. We show that the S^2xS^1 partition functions of some known 3d Seiberg-like dualities reduce, in a…

We establish a coupling between the $\mathcal{P}(\phi)_2$ measure and the Gaussian free field on the two-dimensional unit torus at all spatial scales, quantified by probabilistic regularity estimates on the difference field. Our result…