Related papers: Conformal Differential Operator in Embedding Space…
The class of effective actions exactly reproducing the conformal anomaly in 4D is considered. It is demonstrated that the freedom within this class can be fixed by the choice of the conformal gauge. The conformal invariant part of the…
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
We study a family of semiample divisors on $\bar{M}_{0,n}$ defined using conformal blocks and analyze their associated morphisms.
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
We present Bernstein-Sato identities for scalar-, spinor- and differential form-valued distribution kernels on Euclidean space associated to conformal symmetry breaking operators. The associated Bernstein-Sato operators lead to partially…
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 develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is analyzed in radial quantization: individual…
We study various aspects of half-BPS surface defect operators in $\mathcal{N}=4$ SYM. For defects on generic points on the moduli space we use superconformal symmetry to fix the form of one-point and two-point functions of half-BPS…
In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…
In this work, we exploit the operator content of the $(D_{4}, A_{6})$ conformal algebra. By constructing a $Z_{2}$-invariants fusion rules of a chosen subalgebra and by resolving the bootstrap equations consistent with these rules, we…
We use supershadow methods to derive new expressions for superconformal blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the four-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be…
Let ${\cal D}^k$ be the space of $k$-th order linear differential operators on ${\bf R}$: $A=a_k(x)\frac{d^k}{dx^k}+\cdots+a_0(x)$. We study a natural 1-parameter family of $\Diff(\bf R)$- (and $\Vect(\bf R)$)-modules on ${\cal D}^k$. (To…
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…
We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable…
For a vertex operator algebra $V$, one may naturally define spaces of conformal blocks following a construction of Frenkel-Ben-Zvi generalized by Damiolini-Gibney-Tarasca. If $V$ is strongly rational, these spaces of conformal blocks form…
The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential…
The aim of this paper is to study a Lie conformal algebra of Block type. In this paper, conformal derivation, conformal module of rank 1 and low-dimensional comohology of the Lie conformal algebra of Block type are studied. Also, the vertex…
We obtain infinitely many boundary operators in the Brownian loop soup in the subcritical phase by analyzing the conformal block expansion of the two-point function that computes the probability of having two marked points on the upper…