Related papers: The operator algebra of cyclic orbifolds
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
We study correlation functions of single-cycle chiral operators in the symmetric product orbifold of N supersymmetric four-tori. Correlators of twist operators are evaluated on covering surfaces, generally of different genera, where fields…
We construct a family of intertwining operators (screening operators) between various Fock space modules over the deformed $W_n$ algebra. They are given as integrals involving a product of screening currents and elliptic theta functions. We…
We study $\mathcal{O}$-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of $\mathcal{O}$-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter…
We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…
We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this…
At large N, a field theory and its orbifolds (given by projecting out some of its fields) share the same planar graphs. If the parent-orbifold relation continues even nonperturbatively, then properties such as confinement and chiral…
We establish an operator--theoretic correspondence between periodic Bernoulli kernels and Hermite polynomials, framed through the umbral calculus and a quantum analogy. Starting from the analytic master function $F^\ast$, the periodic…
We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however,…
We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral…
We introduce a full set of rules to directly express all $M$-point conformal blocks in one- and two-dimensional conformal field theories, irrespective of the topology. The $M$-point conformal blocks are power series expansion in some…
We study the spectrum generating closed nonlinear superconformal algebra that describes $\mathcal{N}=2$ super-extensions of rationally deformed quantum harmonic oscillator and conformal mechanics models with coupling constant $g=m(m+1)$,…
We give a simple geometric characterization of isospectral orbifolds covered by spheres, complex projective spaces and the quaternion projective line having cyclic fundamental group. The differential operators considered are…
We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…
We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces a vertex…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid…
The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions of one string propagating in space-time splitting into n strings in conformal field theory. This notion is in some sense dual to…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…