Related papers: Liouville Quantum Duality and Random Planar Maps
We examine a possibility to introduce a non-trivial classical background metric into the 2-d Liouville gravity theory. The classical background appears as a part of the Weyl factor of the physical metric of 2-d surfaces with some conformal…
We construct a conformal welding of two Liouville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm-Loewner evolution (SLE), thereby resolving a variant of a conjecture of…
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A_q integrable hierarchy via the resonance transformations, which are in turn…
Large $N$ matrix models modified by terms of the form $ g(\Tr\Phi^n)^2$ generate random surfaces which touch at isolated points. Matrix model results indicate that, as $g$ is increased to a special value $g_t$, the string susceptibility…
We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern…
We derive the conformal Ward identities for the correlation functions of the Stress--Energy tensor in probabilistic Liouville Conformal Field Theory on compact Riemann surfaces by varying the correlation functions with respect to the…
We analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several classes of cubic…
The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double-scaling limit of the recursion relation…
Can you hear the shape of Liouville quantum gravity? We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the $n$-th eigenvalue grows linearly with $n$, with the proportionality constant given by the Liouville area of the…
Liouville conformal field theory describes a random geometry that fluctuates around a deterministic one: the unique solution of the problem of finding, within a given conformal class, a Riemannian metric with prescribed scalar and geodesic…
We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which corresponds to central charge values $\mathbf c_{\mathrm L} \in…
We study the double- and triple-scaling limits of a complex multi-matrix model, with $\mathrm{U}(N)^2\times \mathrm{O}(D)$ symmetry. The double-scaling limit amounts to taking simultaneously the large-$N$ (matrix size) and large-$D$ (number…
We study Liouville quantum gravity (LQG) surfaces whose law has been reweighted according to nesting statistics for a conformal loop ensemble (CLE) relative to $n\in \mathbb{N}_0$ marked points $z_1,\dots,z_n$. The idea is to consider a…
We extend the study of relevant deformations connecting 2d (0,2) gauge theories on D1-branes probing toric Calabi-Yau 4-folds beyond pure mass deformations. The underlying geometry provides powerful insights when field-theoretic tools are…
We give a concise presentation of the construction of the Liouville quantum gravity (LQG) eigenvalues and eigenfunctions, i.e., the spectrum associated to the infinitesimal generator of Liouville Brownian motion, the canonical diffusion in…
We revisit the problem of hard particles on planar random tetravalent graphs in view of recent combinatorial techniques relating planar diagrams to decorated trees. We show how to recover the two-matrix model solution to this problem in…
The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of…
General properties of perturbed conformal field theory interacting with quantized Liouville gravity are considered in the simplest case of spherical topology. We discuss both short distance and large distance asymptotic of the partition…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
By employing Aronsson's Absolute Minimizers of $L^\infty$ functionals, we prove that Absolutely Minimizing Maps $u:\R^n \larrow \R^N$ solve a "tangential" Aronsson PDE system. By following Sheffield-Smart \cite{SS}, we derive $\De_\infty$…