737 research outputs found
Generalised Moonshine and Abelian Orbifold Constructions
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 MCFT and Abelian orbifold constructions of MCFTs and summarise some
of the relevant physics lore surrounding such constructions including aspects
of the modular group, the fusion algebra and the notion of a self-dual MCFT.
The FLM Moonshine Module, , is historically the first example of
such a construction being a orbifolding of the Leech lattice MCFT,
. We review the usefulness of these ideas in understanding Monstrous
Moonshine, the genus zero property for Thompson series which we have shown is
equivalent to the property that the only meromorphic orbifoldings of
are and itself (assuming that
is uniquely determined by its characteristic function .
We show that these constraints on the possible orbifoldings of
are also sufficient to demonstrate the genus zero property for
Generalised Moonshine functions in the simplest non-trivial prime cases by
considering orbifoldings of . Thus Monstrous
Moonshine implies Generalised Moonshine in these cases.Comment: Talk presented at the AMS meeting on Moonshine, the Monster and
related topics, Mt. Holyoke, June 1994, 16 pp, Plain TeX with AMS Font
Some Generalizations of the MacMahon Master Theorem
We consider a number of generalizations of the -extended MacMahon
Master Theorem for a matrix. The generalizations are based on replacing
permutations on multisets formed from matrix indices by partial permutations or
derangements over matrix or submatrix indices.Comment: 16 pages, 4 figure
The Virasoro Algebra and Some Exceptional Lie and Finite Groups
We describe a number of relationships between properties of the vacuum Verma
module of a Virasoro algebra and the automorphism group of certain vertex
operator algebras. These groups include the Deligne exceptional series of
simple Lie groups and some exceptional finite simple groups including the
Monster and Baby Monster.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Monstrous Moonshine and the uniqueness of the Moonshine module
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 discuss some evidence to support the uniqueness of the Moonshine
module by considering possible alternative orbifold constructions from a Leech
lattice compactified string. Within these constructions we find a new
relationship between the centralisers of the Monster group and the Conway group
generalising an observation made by Conway and Norton. We also relate the
uniqueness of the Moonshine module to Monstrous Moonshine and argue that given
this uniqueness, then the genus zero properties hold if and only if orbifolding
the Moonshine module with respect to a Monster element reproduces the Moonshine
module or the Leech theory. (Talk presented at the Nato Advanced Research
Workshop on `Low dimensional topology and quantum field theory`, Cambridge,
6-13 Sept 1992)Comment: 12 pages, DIAS-STP-92-2
Vertex Algebras According to Isaac Newton
We give an introduction to vertex algebras using elementary forward
difference methods originally due to Isaac Newton.Comment: 20 page
Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I
We define the partition and -point functions for a vertex operator algebra
on a genus two Riemann surface formed by sewing two tori together. We obtain
closed formulas for the genus two partition function for the Heisenberg free
bosonic string and for any pair of simple Heisenberg modules. We prove that the
partition function is holomorphic in the sewing parameters on a given suitable
domain and describe its modular properties for the Heisenberg and lattice
vertex operator algebras and a continuous orbifolding of the rank two fermion
vertex operator super algebra. We compute the genus two Heisenberg vector
-point function and show that the Virasoro vector one point function
satisfies a genus two Ward identity for these theories.Comment: 57 Pages, 5 figures. This is an extended version of roughly one half
of arXiv:0712.062
Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II
We continue our program to define and study -point correlation functions
for a vertex operator algebra on a higher genus compact Riemann surface
obtained by sewing surfaces of lower genus. Here we consider Riemann surfaces
of genus 2 obtained by attaching a handle to a torus. We obtain closed formulas
for the genus two partition function for free bosonic theories and lattice
vertex operator algebras . We prove that the partition function is
holomorphic in the sewing parameters on a given suitable domain and describe
its modular properties. We also compute the genus two Heisenberg vector
-point function and show that the Virasoro vector one point function
satisfies a genus two Ward identity. We compare our results with those obtained
in the companion paper, when a pair of tori are sewn together, and show that
the partition functions are not compatible in the neighborhood of a two-tori
degeneration point. The \emph{normalized} partition functions of a lattice
theory \emph{are} compatible, each being identified with the genus two
theta function of .Comment: 51 pages, 3 figure
- …