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

We study the extensions of two left modules $W_1, W_2$ for a meromorphic open-string vertex algebra $V$. We show that the extensions satisfying some technical but natural convergence conditions are in bijective correspondence to the first…

In this paper we discuss the structure of the tensor product V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series and irreducible highest weight module over the Virasoro algebra. We generalize Zhang's…

We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.

The classical theory of monstrous moonshine describes the unexpected connection between the representation theory of the monster group $M$, the largest of the simple sporadic groups, and certain modular functions, called Hauptmodln. In…

We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in…

Recent work has related the equivariant elliptic genera of sigma models with K3 surface target to a vertex operator superalgebra that realizes moonshine for Conway's group. Motivated by this we consider conditions under which a self-dual…

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$-isometry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for…

We propose a conjecture that is a substantial generalization of the genus zero assertions in both Monstrous Moonshine and Modular Moonshine. Our conjecture essentially asserts that if we are given any homomorphism to the complex numbers…

For certain subgroups of $M_{24}$, we give vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms. These meromorphic Jacobi forms are canonically associated to the mock modular forms of…

We use uniqueness of a VOA (vertex operator algebra) extension of $(V_{EE_8}^+)^3$ to a Moonshine type VOA to give a new existence proof of a finite simple group of Monster type. The proof is relatively direct. Our methods depend on VOA…

We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the…

The category of weight modules $L_k(\mathfrak{sl}_2)\text{-wtmod}$ of the simple affine vertex algebra of $\mathfrak{sl}_2$ at an admissible level $k$ is neither finite nor semisimple and modules are usually not lower-bounded and have…

We construct orbifolds of holomorphic lattice Vertex Operator Algebras for non-Abelian finite automorphism groups $G$. To this end, we construct twisted modules for automorphisms $g$ together with the projective representation of the…

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we…

We consider the application of Abelian orbifold constructions in Meromorphic Conformal Field Theory (MCFT) towards an understanding of various aspects of Monstrous Moonshine and Generalised Moonshine. We review some of the basic concepts in…

We study a special class of holomorphic vertex operator algebras (VOAs) that we call \emph{balanced}.\ For a balanced, holomorphic VOA $V=\mathbb{C}\mathbf{1}\oplus V_1\oplus\dots$ with $c=32$ or $40$ we show that the Virasoro vectors of…

Let $M$ be a Riemannian manifold. For $p\in M$, the tensor algebra of the negative part of the (complex) affinization of the tangent space of $M$ at $p$ has a natural structure of a meromorphic open-string vertex algebra. These meromorphic…

Modules over affine Lie superalgebras ${\cal G}$ are studied, in particular, for ${\cal G}=\hat{OSP(1,2)}$. It is shown that on studying Verma modules, much of the results in Kac-Moody algebra can be generalized to the super case. Of most…

Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They…