Related papers: Topological modularity of Monstrous Moonshine
We consider the relationship between the conjectured uniqueness of the Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first…
We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order $p=2,3,5,7$ and the other of order $pk$ for $k=1$ or $k$ prime. We show that…
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…
The theory of topological modular forms (TMF) predicts that elliptic genera of physical theories satisfy a certain divisibility property, determined by the theory's gravitational anomaly. In this note we verify this prediction in Duncan's…
In these notes, based on lectures given in Istanbul, we give an introduction both to Monstrous Moonshine and to the classification of rational conformal field theories, using this as an excuse to explore several related structures and go on…
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…
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 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…
We determine the space of 1-point correlation functions associated with the Moonshine module: they are precisely those modular forms of non-negative integral weight which are holomorphic in the upper half plane, have a pole of order at most…
In this talk we consider the relationship between the conjectured uniqueness of the Moonshine module of Frenkel, Lepowsky and Meurman and Monstrous Moonshine, the genus zero property for Thompson series discovered by Conway and Norton. We…
Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. The celebrated observations that 196884=1+196883 and 21493760=1+196883+21296876, etc., illustrate the case of the modular function…
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…
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case…
We analyze aspects of extant examples of 2d extremal chiral (super)conformal field theories with $c\leq 24$. These are theories whose only operators with dimension smaller or equal to $c/24$ are the vacuum and its (super)Virasoro…
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…
We verify the Generalised Moonshine conjectures for some irrational modular functions for the Monster centralisers related to the Harada-Norton, Held, $M_{12}$ and $L_3(3)$ simple groups based on certain orbifolding constraints. We find…
We consider the application of permutation orbifold constructions towards a new possible understanding of the genus zero property in Monstrous and Generalized Moonshine. We describe a theory of twisted Hecke operators in this setting and…
Monstrous Moonshine was extended in two complementary directions during the 1980s and 1990s, giving rise to Norton's Generalized Moonshine conjecture and Ryba's Modular Moonshine conjecture. Both conjectures have been unconditionally…
The Moonshine module is a $c=24$ conformal field theory (CFT) whose automorphism group is the Monster group. It was argued by Dixon, Ginsparg, and Harvey in \cite{Dixon:1988qd} that there exists a spin lift of the Moonshine CFT with…