Lie Conformal Algebra and Dual Pair Type Realizations of Some Moonshine Type VOAs, and Calculations of the Correlation Functions

A new construction of the moonshine vertex operator algebra over the real number field

We give a new construction of the moonshine VOA V^{\natural} over the real number field. We proved that V^{\natural} has a positive definite invariant bilinear form and its full automorphism group is the Monster simple group. We also construct an infinite series of meromorphic VOAs whose full automorphism groups are finite. We calculate the trace form on V^{\natural} for some element of the Monster.

自对偶顶点算子超代数与宝贝怪兽 (Self-dual Vertex Operator Super Algebras and the Baby Monster)

Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster)

本文研究自对偶顶点算子超代数，构造中心荷23.5的较短月光模，宝贝怪兽群作用其上，并引入极值SVOAs概念，给出存在性结果。

VOAs labelled by complex reflection groups and 4d SCFTs

We define and study a class of $\mathcal{N}=2$ vertex operator algebras $\mathcal{W}_{\mathcal{\mathsf{G}}}$ labelled by complex reflection groups. They are extensions of the $\mathcal{N}=2$ super Virasoro algebra obtained by introducing additional generators, in correspondence with the invariants of the complex reflection group $\mathcal{\mathsf{G}}$. If $\mathcal{\mathsf{G}}$ is a Coxeter group, the $\mathcal{N}=2$ super Virasoro algebra enhances to the (small) $\mathcal{N}=4$ superconformal algebra. With the exception of $\mathcal{\mathsf{G}} = \mathbb{Z}_2$, which corresponds to just the $…

Realizations of the Monster Lie algebra

We study aspects of the theory of generalized Kac-Moody Lie algebras (or Borcherds algebras) and their standard modules. It is shown how such an algebra with no mutually orthogonal imaginary simple roots, including Borcherds' Monster Lie algebra $\frak m$, can be naturally constructed from a certain Kac-Moody subalgebra and a module for it. We observe that certain generalized Verma (induced) modules for generalized Kac-Moody algebras are standard modules and hence irreducible. In particular, starting from the moonshine module for the Monster group $M$, we construct a certain $\{frak gl}_2$- an…

仿射 $\mathcal{W}$-代数与来自三维 $\mathcal N=4$ 非阿贝尔箭图规范理论的 Miura 映射

Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal N=4$ non-Abelian quiver gauge theories

本文研究三维 $\mathcal{N}=4$ 线性箭图规范理论 H-扭转得到的顶点算子代数，揭示其与希格斯分支及仿射 $\mathcal{W}$-代数的关系，并提出箭图约化算法以系统构造新自由场实现。

Plane Partition Realization of (Web of) W-algebra Minimal Models

Recently, Gaiotto and Rapcak (GR) proposed a new family of the vertex operator algebra (VOA) as the symmetry appearing at an intersection of five-branes to which they refer as Y algebra. Prochazka and Rapcak, then proposed to interpret Y algebra as a truncation of affine Yangian whose module is directly connected to plane partitions (PP). They also developed GR's idea to generate a new VOA by connecting plane partitions through an infinite leg shared by them and referred it as the web of W-algebra (WoW). In this paper, we demonstrate that double truncation of PP gives the minimal models of suc…