Related papers: Monstrous moonshine and the classification of CFT
This article is a short and elementary introduction to the monstrous moonshine aiming to be as accessible as possible. I first review the classification of finite simple groups out of which the monster naturally arises, and features of the…
We explore connections among Monstrous Moonshine, orbifolds, the Kitaev chain and topological modular forms. Symmetric orbifolds of the Monster CFT, together with further orbifolds by subgroups of Monster, are studied and found to satisfy…
We present a family of conformal field theories (or candidates for CFTs) that is build on extremal partition functions. Spectra of these theories can be decomposed into the irreducible representations of the Fischer-Griess Monster sporadic…
The word moonshine refers to unexpected relations between the two distinct mathematical structures: finite group representations and modular objects. It is believed that the key to understanding moonshine is through physical theories with…
Twenty-five years ago, Conway and Norton published their remarkable paper `Monstrous Moonshine', proposing a completely unexpected relationship between finite simple groups and modular functions. This paper reviews the progress made in…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
Recent work on the classification of conformal field theories with one primary field (the identity operator) is reviewed. The classification of such theories is an essential step in the program of classification of all rational conformal…
These notes provide an elementary (and incomplete) sketch of the objects and ideas involved in monstrous and umbral moonshine. They were the basis for a plenary lecture at the 18th International Congress on Mathematical Physics, and for a…
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
We describe the finite subgraph $\mathfrak{M}$ of Conway's Big Picture required to describe all $171$ genus zero groups appearing in monstrous moonshine. We determine the local structure of $\mathfrak{M}$ and give a purely group-theoretic…
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work we continue this program, with a focus on the two smallest…
This lecture note covers topics on boundary conformal field theory, modular transformations and the Verlinde formula, and boundary logarithmic CFT. An introductory review on CFT with boundary and a discussion of its applications to…
We study replication identities satisfied by conformal characters of a 2D CFT, providing a natural framework for a physics interpretation of the famous Hauptmodul property of Monstrous Moonshine, and illustrate the underlying ideas in…
We introduce a notion of Hecke-monicity for functions on certain moduli spaces associated to torsors of finite groups over elliptic curves, and show that it implies strong invariance properties under linear fractional transformations.…
Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…
In recent literature, moonshine has been explored for some groups beyond the Monster, for example the sporadic O'Nan and Thompson groups. This collection of examples may suggest that moonshine is a rare phenomenon, but a fundamental and…
We describe surprising relationships between automorphic forms of various kinds, imaginary quadratic number fields and a certain system of six finite groups that are parameterised naturally by the divisors of twelve. The Mathieu group…
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,…
In this article, we discuss the relation between Kac-Moody algebras, the monstrous moonshine, Jacobi forms and infinite products. We also review Borcherds' solution of the Moonshine Conjecture and his work of constructing automorphic forms…
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…