Related papers: Radial Coordinates for Conformal Blocks

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 initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which…

Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to…

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…

The correlators of free four dimensional conformal field theories (CFT4) have been shown to be given by amplitudes in two-dimensional $so(4,2)$ equivariant topological field theories (TFT2), by using a vertex operator formalism for the…

In the context of Conformal Field Theory (CFT), many results can be obtained from the representation theory of the Virasoro algebra. While the interest in Logarithmic CFTs has been growing recently, the Virasoro representations…

The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field…

Conformal algebra is an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality…

We consider mixed four-point correlators of 1/2-BPS operators $\mathcal{O}_{k}$ in the maximally supersymmetric CFTs, i.e. the 3d $\mathcal{N}=8$, 4d $\mathcal{N}=4$, and 6d $\mathcal{N}=(2,0)$ theories. In arXiv:hep-th/0405180, Dolan,…

Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…

We show that the path-integral of conformal field theories in $D$ dimensions (CFT$_D$) can be constructed by solving for eigenstates of an RG operator following from the Turaev-Viro formulation of a topological field theory in $D+1$…

We realize any space of conformal blocks attached to a punctured curve inside the cohomology of a configuration space of that curve and compare the WZW connection with the Gauss-Manin connection.

This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…

Let M(r) be the moduli space of rank r vector bundles with trivial determinant on a Riemann surface X . This space carries a natural line bundle, the determinant line bundle L . We describe a canonical isomorphism of the space of global…

We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the…

We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations…

We introduce a class of polynomials that we call fused Specht polynomials and use them to characterize irreducible representations of the fused Hecke algebra with parameter $q=-1$ in the space of polynomials. We apply the fused Specht…

The Bootstrap approach to calculating cosmological correlators relies on a well motivated ansatz. It is typical in the literature to assume that correlators are rational functions as this greatly increases our constraining power. However,…

In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe…