相关论文: Conformal Blocks: Vector bundle structures, Sewing…
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…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
We study a family of semiample divisors on $\bar{M}_{0,n}$ defined using conformal blocks and analyze their associated morphisms.
These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…
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 report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.
This paper begins with a brief survey of the period prior to and soon after the creation of the theory of vertex operator algebras (VOAs). This survey is intended to highlight some of the important developments leading to the creation of…
Let $\mathbb V$ be an $\mathbb N$-graded, $C_2$-cofinite vertex operator algebra (VOA) admitting a non-lowest generated module in $\mathrm{Mod}(\mathbb V)$ (e.g., the triplet algebras $\mathcal{W}_p$ for $p\in \mathbb{Z}_{\geq 2}$ or the…
These notes are from courses given at TASI and the Advanced Strings School in summer 2015. Starting from principles of quantum field theory and the assumption of a traceless stress tensor, we develop the basics of conformal field theory,…
Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have…
We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodchikov equations constructed earlier by the second and third…
These are lecture notes for a course in Winter 2022/23, updated and completed in October 2025. The goal of the lectures is to present some recent developments around six-functor formalisms, in particular: the abstract theory of 6-functor…
Conformal blocks in odd spacetime dimensions are not known in closed analytic form. To facilitate efficient computations in the conformal bootstrap, we introduce $\texttt{GoBlocks}$: a novel conformal-block generator implemented in the Go…
We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…
This is a survey paper: we discuss certain recent results, with some improvements. It will appear in the S. Cruz proceedings.
We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group…