Related papers: Vertex algebras, topological defects, and Moonshin…

This paper is a continuation of our paper math.QA/0403010 at which several coset subalgebras of the lattice VOA $V_{\sqrt{2}E_8}$ were constructed and the relationship between such algebras with the famous McKay observation on the extended…

We generalize the Carpi-Kawahigashi-Longo-Weiner correspondence between vertex operator algebras and conformal nets to the case of vertex operator superalgebras and graded-local conformal nets by introducing the notion of strongly…

Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…

Certain vertex operator algebras have integral forms (integral spans of bases which are closed under the countable set of products). It is unclear when they (or integral multiples of them) are integral as lattices under the natural bilinear…

In this article, we study the moonshine vertex operator algebra starting with the tensor product of three copies of the vertex operator algebra $V_{\sqrt2E_8}^+$, and describe it by the quadratic space over $\F_2$ associated to…

Given a collection of modules of a vertex algebra parametrized by an abelian group, together with one dimensional spaces of composable intertwining operators, we assign a canonical element of the cohomology of an Eilenberg-Mac Lane space.…

We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy. Our Main Theorem…

We construct super vertex operator algebras which lead to modules for moonshine relations connecting the four smaller sporadic simple Mathieu groups with distinguished mock modular forms. Starting with an orbifold of a free fermion theory,…

For certain vertex operator algebras (e.g., lattice type) and given finite group of automorphisms, we prove existence of a positive definite integral form invariant under the group. Applications include an integral form in the Moonshine VOA…

We associate to any holomorphic vertex algebra a collection of Teichm\"{u}ller modular forms, one in each genus. In genus one we obtain the character of the vertex algebra, and we thus reprove Zhu's modularity result. In higher genus, we…

In this article, we show that a framed vertex operator algebra V satisfying the conditions: (1) V is holomorphic (i.e., V is the only irreducible V-module); (2) V is of rank 24; and (3) V_1=0; is isomorphic to the moonshine vertex operator…

We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III_1) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In…

Let $V$ be a strongly regular vertex operator algebra and let $\frak{ch}_V$ be the space spanned by the characters of the irreducible $V$-modules.\ It is known that $\frak{ch}_V$ is the space of solutions of a so-called \emph{modular linear…

We provide a lattice regularization of all topological defects in minimal models CFTs using RSOS and anyonic spin chains. For defects of type $(1,s)$, we connect our result with the "topological symmetry" initially identified in Fibonacci…

We construct a new cohomology functor from the a certain category of {\it quantum operator algebras} to the category of {\it Batalin-Vilkovisky algebras}. This {\it Moonshine cohomology} has, as a group of natural automorphisms, the…

A vertex operator algebra of lattice type ADE has a standard integral form which extends a Chevalley basis for its degree 1 Lie algebra. This integral form may be used to define a vertex algebra over a commutative ring $R$ and to get a…

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…

In this article, we study the Ising vectors in the vertex operator algebra $V_\Lambda^+$ associated with the Leech lattice $\Lambda$. The main result is a characterization of the Ising vectors in $V_\Lambda^+$. We show that for any Ising…

We consider topological defect networks with junctions in $A_{N-1}$ Toda CFT and the connection to supersymmetric loop operators in $\mathcal{N} = 2$ theories of class S on a four-sphere. Correlation functions in the presence of topological…

Given a holomorphic $C_2$-cofinite vertex operator algebra $V$ with graded dimension $j-744$, Borcherds's proof of the monstrous moonshine conjecture implies any finite order automorphism of $V$ has graded trace given by a "completely…