Related papers: A conformal bootstrap approach to critical percola…
We derive new constraints on the spectrum of two-dimensional conformal field theories with central charge $c>1.$ Employing the pillow representation of the four point correlator of identical scalars with dimension $\Delta_{\mathcal{O}}$ and…
Conformal blocks are the building blocks for correlation functions in conformal field theories. The four-point function is the most well-studied case. We consider conformal blocks for $n$-point correlation functions. For conformal field…
Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…
Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes…
We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
Virasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide three closed-form expansions for the four-point Virasoro blocks on the sphere, for arbitrary…
The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric aspects of universality. As a case study we…
Critical points and singularities are encountered in the study of critical phenomena in probability and physics. We present recent results concerning the values of such critical points and the nature of the singularities for two prominent…
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…
We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…
Four-point correlation functions of hypermultiplet bilinear composites are analysed in N=2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is…
We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the $d$-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair…
In this thesis, we introduce new tools for the conformal bootstrap, autoboot and qboot. Each tool solves a different step in the whole computational stack, and combined with an existing efficient tool SDPB which solves semidefinite…
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid…
Fitting percolation into the conformal field theory framework requires showing that connection probabilities have a conformally invariant scaling limit. For critical site percolation on the triangular lattice, we prove that the probability…
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…
The N = 2, 4 superconformal symmetry constraints in d = 4 for four point functions of chiral primary 1/2-BPS operators are derived. The operators are described by symmetric traceless tensors of the internal R-symmetry group. A substantial…