Related papers: Confluent Conformal Blocks of the Second Kind

We carefully bootstrap the crossing kernels of Virasoro conformal blocks from first principles. Our approach emphasizes the Hilbert space structure of the space of Virasoro conformal blocks which makes the consistency of crossing…

We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS$_3$/CFT$_2$ correspondence. To give such an interpretation in previous studies, certain restrictions…

Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials. Using this presentation we give a generating set in the space of conformal blocks at any level if the marked…

These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…

In this work we study Liouville conformal blocks with degenerate primaries and one operator in an irregular representation of the Virasoro algebra. Using an algebraic approach, we derive modified BPZ equations satisfied by such blocks and…

For each simply connected, simple complex group $G$ we show that the direct sum of all vector bundles of conformal blocks on the moduli stack $\bar{\mathcal{M}}_{g, n}$ of stable marked curves carries the structure of a flat sheaf of…

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…

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of…

We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of a closed loop with external legs (a necklace sub-diagram)…

To a given algebraic curve we assign an infinite family of quantum curves (Schr\"odinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model…

We construct modular linear differential equations (MLDEs) w.r.t. subgroups of the modular group whose solutions are Virasoro conformal blocks appearing in the expansion of a crossing symmetric 4-point correlator on the sphere. This uses a…

We study conformal blocks (the space of correlation functions) over compact Riemann surfaces associated to vertex operator algebras which are the sum of highest weight modules for the underlying Virasoro algebra. Under the fairly general…

We find a simple relation between two-dimensional BPS N=2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2,2) superconformal theories…

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…

In a previous paper by the authors, we obtain the first example of a finitely freely generated simple $\mathbb Z$-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. In this paper,…

In this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials. To this end, the analysis of…

We show that the conformal blocks constructed in the previous article by the first and the third author may be described as certain integrals in equivariant cohomology. When the bundles of conformal blocks have rank one, this construction…

We develop a calculus of variations for functionals on certain spaces of conformal maps. Such a space \Omega\ is composed of all maps that are conformal on domains containing a fix compact annular set of the Riemann sphere, and that are…

Here we define a series of associative algebras attached to a vertex operator algebra $V$, called mode transition algebras, showing they reflect both algebraic properties of $V$ and geometric constructions on moduli of curves. One can…

We study four types of one-point torus blocks arising in the large central charge regime. According to different limits of conformal dimensions we distinguish between the global block, the light block, the heavy-light block, and the…