Related papers: Double dimers, conformal loop ensembles and isomon…
We define two new models on the square lattice, in which each allowed configuration is a superposition of a covering by ``white'' dimers and one by ``black'' dimers. Each model maps to a solid-on-solid (SOS) model in which the ``height''…
We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency…
The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero…
We reexamine the disorder-dominated multicritical point of the two-dimensional +/-J Ising model, known as the Nishimori point (NP). At the NP we investigate numerically and analytically the behavior of the disorder correlator, familiar from…
This is the first part of a work aimed at constructing the stress-energy tensor of conformal field theory as a local "object" in conformal loop ensembles (CLE). This work lies in the wider context of re-constructing quantum field theory…
Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio \tau. Loops…
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super-Yang-Mills. It is dual to another complex matrix…
We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
We consider a full Leigh-Strassler deformation of the ${\cal N}=4$ SYM theory and look for conditions under which the theory would be conformally invariant and finite. Applying the algorithm of perturbative adjustments of the couplings we…
Correlators of a certain one-dimensional superconformal field theory dual to hypermultiplets in AdS$_2\times$S$^2$ exhibit a hidden four-dimensional conformal symmetry which allows one to repackage all tree-level 4-point correlators into a…
Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of…
Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited…
We use the method of discrete loop equations to calculate exact correlation functions of spin and disorder operators on the sphere and on the boundary of a disk in the $c = 1/2$ string, both in the Ising and dual Ising matrix model…
We present a detailed study of various aspects of Spinor-Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the…
We demonstrate by explicit multi-loop calculation that \gamma-deformed planar N=4 SYM, supplemented with a set of double-trace counter-terms, has two nontrivial fixed points in the recently proposed double scaling limit, combining vanishing…
We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of…
Renormalization group evolution of QCD composite light-cone operators, built from two and more quark and gluon fields, is responsible for the logarithmic scaling violations in diverse physical observables. We analyze spectra of anomalous…