Related papers: Graph theoretical approach to conformal correlator…
We determine central charges, critical exponents and appropriate gradient flow relations for nonsupersymmetric vector-like and chiral Gauge-Yukawa theories that are fundamental according to Wilson and that feature calculable UV or IR…
Graph is a useful data structure to model various real life aspects like email communications, co-authorship among researchers, interactions among chemical compounds, and so on. Supporting such real life interactions produce a knowledge…
The analysis of data such as graphs has been gaining increasing attention in the past years. This is justified by the numerous applications in which they appear. Several methods are present to predict graphs, but much fewer to quantify the…
In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie…
The quantum dynamics of the gravitational field non-minimally coupled to an (also dynamical) scalar field is studied in the {\em broken phase}. For a particular value of the coupling the system is classically conformal, and can actually be…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
We consider $\mathcal{N}=2$ superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted…
From conformal field theory on the Riemann sphere, we implement its boundary version in a simply-connected domain using the Schottky double construction. We consider the statistical fields generated by background charge modification of the…
Let $G=C_{n}(S)$ be a circulant graph on $n$ vertices. In this paper we characterize chordal circulant graphs and then we compute $\nu (G)$, the induced matching number of $G$. These latter are useful in bounding the Castelnuovo-Mumford…
The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Graph Neural Networks have achieved remarkable accuracy in semi-supervised node classification tasks. However, these results lack reliable uncertainty estimates. Conformal prediction methods provide a theoretical guarantee for node…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent…
Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and…
In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained as a coupling…
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…
Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence…
Conformal fields are a recently discovered class of representations of the algebra of vector fields in $N$ dimensions. Invariant first-order differential operators (exterior derivatives) for conformal fields are constructed.