Vertex operator algebra theory is a new area of mathematics. It has been an exciting and
ever-growing subject from the beginning, starting even before R. Borcherds introduced the …

Vertex algebras are algebraic objects that encapsulate the concept of operator product
expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming …

A bstract We find closed-form expressions for the Schur indices of 4d\(\mathcal {N}\)= 2*
super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas …

Moonshine forms a way of explaining the mysterious connection between the monster finite
group and modular functions from classical number theory. The theory has evolved to …

Abstract Eguchi, Ooguri and Tachikawa observed that the coefficients of the elliptic genus of
type II string theory on K3 surfaces appear to be dimensions of representations of the largest …

For a proper scheme X with a fixed 1–perfect obstruction theory E∙, we define virtual versions
of holomorphic Euler characteristic, χ− y–genus and elliptic genus; they are deformation …

Vertex operators appeared in the early days of string theory as local operators describing
propagation of string states. Mathematical analogues of these operators were discovered in …

The notions of orbifold elliptic genus and elliptic genus of singular varieties are introduced,
and the relation between them is studied. The elliptic genus of singular varieties is given in …

The Mathieu twisted twining genera, ie the analogues of Norton's generalised Moonshine
functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the …

On any Calabi-Yau manifold X one can define a certain sheaf of chiral N= 2 superconformal
field theories, known as the chiral de Rham complex of X. It depends only on the complex …