Related papers: Conformal blocks divisors on $\bar{M}_{0,n}$ from …

We construct and study a family of toric degenerations of the algebra of conformal blocks for a stable marked curve $(C, \vec{p})$ with structure group $SL_3(\mathbb{C}).$ We find that this algebra is Gorenstein. For the genus $0, 1$ cases…

Let $X$ be a smooth, pointed Riemann surface of genus zero, and $G$ a simple, simply-connected complex algebraic group. Associated to a finite number of weights of $G$ and a level is a vector space called the space of conformal blocks, and…

We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the…

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…

Let $L$ be a Lie algebra of Block type over $\C$ with basis $\{L_{\alpha,i}\,|\,\alpha,i\in\Z\}$ and brackets $[L_{\alpha,i},L_{\beta,j}]=(\beta(i+1)-\alpha(j+1))L_{\alpha+\beta,i+j}$. In this paper, we shall construct a formal distribution…

We derive expressions for conformal blocks involving operators with arbitrary spins in 3-dimensional CFTs. We use previous results on the action of the OPE in the embedding space to derive the conformal blocks. The blocks are given as…

We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called `seed blocks' in three…

We survey some recent work on conformal blocks in genus zero, focussing on (1) Chern classes, global generation and morphisms, and (2) the Knizhnik--Zamolodchikov connection on conformal blocks (and invariants), their motivic realizations,…

By way of intersection theory on $\bar M_{g,n}$, we show that geometric interpretations for conformal blocks, as sections of ample line bundles over projective varieties, do not have to hold at points on the boundary. We show such a…

In this work, we study a family of vector bundles on the moduli space of curves constructed from representations of $\text{Vir}_{2k+1,2}$, a family of vertex operator algebras derived from the Virasoro Lie algebra. Using the relationship…

For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector…

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 find a five-parameter family of partial differential systems in two variables with two polynomial Hamiltonians. We give its symmetry and holomorphy conditions. These symmetries, holomorphy conditions and invariant divisors are new.

Here we consider higher Chern classes of vector bundles of conformal blocks on $\overline{\operatorname{M}}_{0,n}$, giving explicit formulas for them, and extending various results that hold for first Chern classes to them. We use these…

Suppose $l,m$ are natural numbers with $l\le m$, and $\mathbb{F}$ a field of characteristic $p$, and let $\mathcal{C}_{l,m}^{\mathbb{F}}$ denote the centraliser of the group algebra $\mathbb{F}S_l$ inside $\mathbb{F}S_m$. Ellers and Murray…

For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…

Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants…

We introduce polyhedral cones associated with $m$-hemimetrics on $n$ points, and, in particular, with $m$-hemimetrics coming from partitions of an $n$-set into $m+1$ blocks. We compute generators and facets of the cones for small values of…

In this article, we find a $q$-analogue for Fomin's formulas. The original Fomin's formulas relate determinants of random walk excursion kernels to loop-erased random walk partition functions, and our formulas analogously relate conformal…

For distinct complex numbers $z_1,...,z_{2N}$, we give a polynomial $P(y_1,...,y_{2N})$ in the variables $y_1,...,y_{2N}$, which is homogeneous of degree $N$, linear with respect to each variable, $sl_2$-invariant with respect to a natural…