Related papers: Gaussian Free Fields and KPZ Relation in R^4

In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov. Our approach follows the construction carried out by the authors together with A. Kupiainen in…

We present a new construction of the Euclidean $\Phi^4$ quantum field theory on $\mathbb{R}^3$ based on PDE arguments. More precisely, we consider an approximation of the stochastic quantization equation on $\mathbb{R}^3$ defined on a…

We show that the Horava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this…

We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N=2 gauge theories. Our construction naturally involves four-dimensional theories with…

In the canonical approach to Lorentzian Quantum General Relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of an appropriate…

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…

In this paper we consider an extended Gauss-Bonnet gravity theory in arbitrary dimensions and in a space provided with a Weyl connection, which is torsionless but not metric-compatible, the non-metricity tensor being determined by a vector…

We show that the rescaled maximum of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3 is in the maximal domain of attraction of the Gumbel distribution. The result holds both for the infinite-volume field as well as…

We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When…

This text is a survey (Bourbaki seminar) on the paper "Liouville quantum gravity and KPZ" By B.Duplantier and S.Sheffield. The study of statistical physics models in two dimensions (d=2) at their critical point is in general a significantly…

We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by…

We study an extension of symmetric teleparallel gravity i.e. Weyl-type $f(Q,T)$ gravity and the divergence-free parametrization of the deceleration parameter $q(z) = q_{0}+q_{1}\frac{z(1+z)}{1+z^2}$ ($q_{0}$ and $q_{1}$ are free constants)…

We study Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which has background charge $Q \in (0,2)$ and central charge $\mathbf{c}_{\mathrm{L}} = 1+6Q^2 \in (1,25)$. Recent works have shown how to define…

A scalar field theory with 4-derivative kinetic terms and 4-derivative cubic and quartic couplings is presented as a proxy for quantum quadratic gravity (QQG). The scalar theory is renormalizable and asymptotically free and the remaining…

We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal…

We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kaehler formalism where the basic quantum field is the (Laplacian of the) Kaehler potential. We do a careful first-principles computation of the fixed-area…

We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a…

We study a determinantal Coulomb gas in the complex plane associated with the external potential $$ Q(z)=\frac{1}{1-\tau^2}\big(|z|^2-\tau \text{Re } z^2\big)-2c\log|z-a|, $$ where $\tau\in[0,1)$, $c\ge0$, and $a\ge0$. In the regimes where…

Let $h$ be a log-correlated Gaussian field on $\R^d$, let $\gamma \in (0,\sqrt{2d}),$ let $\mu_h$ be the $\gamma$-Gaussian multiplicative chaos measure, and let $D_h$ be an exponential metric associated with $h$ satisfying certain natural…

We show that, in four-dimensional spacetimes with an arbitrary Einstein metric, with and without a cosmological constant, perturbative dynamical degrees of freedom in generic quadratic-curvature gravity can be decoupled into massless and…