Related papers: From combinatorial maps to correlation functions i…

We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…

A family of models for fluctuating loops in a two dimensional random background is analyzed. The models are formulated as O(n) spin models with quenched inhomogeneous interactions. Using the replica method, the models are mapped to the…

We discuss the geometrical connection between 2D conformal field theories, random walks on hyperbolic Riemann surfaces and knot theory. For the wide class of CFTs with monodromies being the discrete subgroups of SL(2,R), the determination…

The $s$-point correlation function of a Gaussian Hermitian random matrix theory, with an external source tuned to generate a multi-critical singularity, provides the intersection numbers of the moduli space for the $p$-th spin curves…

We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system…

The "bootstrap determination" of the geometrical correlation functions in the two-dimensional Potts model proposed in a paper [arXiv:1607.07224] was later shown in [arXiv:1809.02191] to be incorrect, the actual spectrum of the model being…

We compute the generating functions of a O(n) model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, they were already known, and here we compute all the other topologies. We find that the generating…

The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…

We consider correlation functions in symmetric product orbifold CFTs on the sphere, focusing on the case where all operators are single-cycle twists, and the covering surface is also a sphere. We directly construct the general class of…

Using loop equation technics, we compute all mixed traces correlation functions of the 2-matrix model to large N leading order. The solution turns out to be a sort of Bethe Ansatz, i.e. all correlation functions can be decomposed on…

Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…

We build the Z$_{3}$ invariants fusion rules associated to the (D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-pt correlation functions of critical fields are developed in the…

We investigate correlation functions in a periodic box-ball system. For the two point functions of short distance, we give explicit formulae obtained by combinatorial methods. We give expressions for general N-point functions in terms of…

Four-dimensional N-extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms…

We study the $n$-point functions of scalar multi-trace operators in the $U(N_c)$ gauge theory with adjacent scalars, such as ${\cal N}=4$ super Yang-Mills, at tree-level by using finite group methods. We derive a set of formulae of the…

We consider the O(n) loop model on tetravalent maps and show how to rephrase it into a model of bipartite maps without loops. This follows from a combinatorial decomposition that consists in cutting the O(n) model configurations along their…

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…

In two-dimensional critical loop models, including the $O(n)$ and Potts models, the spectrum is exactly known, as are a few structure constants or ratios thereof. Using numerical conformal bootstrap methods, we study $235$ of the simplest…

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions,…

The simplest examples of chaotic maps are linear, area-preserving maps on the circle, torus, or product of tori; respectively known as the Bernoulli map, the cat map, and the recently introduced "spatiotemporal" cat map. We study…