Related papers: Conformal bootstrap for percolation and polymers
A phase diagram for a surface interacting long flexible partially directed polymer chain in a two-dimensional poor solvent where the possibility of collapse in the bulk exists is determined using exact enumeration method. We used a model of…
AGT correspondence gives an explicit expressions for the conformal blocks of $d=2$ conformal field theory. Recently an explanation of this representation inside the CFT framework was given through the assumption about the existence of the…
We study a supersymmetric theory twisted on a K\"ahler four manifold $M=\Sigma_1 \times \Sigma_2 ,$ where $\Sigma_{1,2}$ are 2D Riemann surfaces. We demonstrate that it possesses a "left-moving" conformal stress tensor on $\Sigma_1$…
We study polymers attached to spherical (circular) or paraboloidal (parabolic) probes in three (two) dimensions. Both self-avoiding and random walks are examined numerically. The behavior of a polymer of size $R_0$ attached to the tip of a…
We study the geometric and physical effects of quadrupolar configurations of disclinations using a conformal metric approach in $(2+1)$ dimensions. Two cases are considered: a linear quadrupole, inducing anisotropic curvature with a…
We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in $4d$ $\mathcal{N}=2$ superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In…
As a simple lattice model that exhibits a phase transition, the Ising model plays a fundamental role in statistical and condensed matter physics. The Ising transition is realized by physical systems, such as the liquid-vapor transition. Its…
These lectures were given at the Weizmann Institute in the spring of 2019. They are intended to familiarize students with the nuts and bolts of the numerical bootstrap as efficiently as possible. After a brief review of the basics of…
We find an infinite set of new noncommuting conserved charges in a specific class of perturbed CFT's and present a criterion for their existence.They appear to be higher momenta of the already known commuting conserved currents.The algebra…
We show that conformal blocks simplify greatly when there is a large difference between two of the scaling dimensions for external operators. In particular the spacetime dimension only appears in an overall constant which we determine via…
We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…
It has long been understood that non-trivial Conformal Field Theories (CFTs) with vanishing central charge ($c=0$) are logarithmic. So far however, the structure of the identity module -- the (left and right) Virasoro descendants of the…
Over the years, problems like percolation and self-avoiding walks have provided important testing grounds for our understanding of the nature of the critical state. I describe some very recent ideas, as well as some older ones, which cast…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field…
Critical systems are described by conformal field theories, whose dynamics can be exactly solved in two dimensions. In the presence of a boundary, with the so-called method of images it is possible to study the surface critical behaviour of…
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All…
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…
Based on transfer matrix techniques and finite size scaling, we study the oriented polymer (self-avoiding walk) with nearest neighbor interaction. In the repulsive regime, various critical exponents are computed and compared with exact…
Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained…