Monstrous Moonshine: Linking the Monster Group to Modular Functions via Vertex Operator Algebras — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Borcherds' proof of Monstrous Moonshine links the Monster group's representation theory to the modular function j(τ) via a vertex operator algebra (VOA) of central charge 24, constructed from the Leech lattice, with the no-ghost theorem from string theory providing the key constraint. | MATH: Central charge c=24; Monster VOA Vnatural with graded dimension ∑n=−1∞ dim(Vnaturaln) qn = j(τ)−744 = q−1+196884q+21493760q2+…; McKay–Thompson series Tg(τ)=∑ tr(g|Vnaturaln)qn−1 are Hauptmoduln for genus-zero groups; Borcherds' denominator identity for the Monster Lie algebra: eρ∏α∈Δ+(1−e−α)mult(α) = j(σ)−j(τ) (where ρ is the Weyl vector, Δ+ positive roots of the Monster Lie algebra, and σ,τ are coordinates on the rank-2 hyperbolic lattice). The no-ghost theorem requires the VOA to have c=24 and be self-dual (holomorphic
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026monstrous,
title = {{Monstrous Moonshine: Linking the Monster Group to Modular Functions via Vertex Operator Algebras — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23553607},
url = {https://zenodo.org/records/23553607},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monstrous Moonshine: Linking the Monster Group to Modular Functions via Vertex Operator Algebras — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23553607
UR - https://zenodo.org/records/23553607
AB - FINDING: Borcherds' proof of Monstrous Moonshine links the Monster group's representation theory to the modular function j(τ) via a vertex operator algebra (VOA) of central charge 24, constructed from the Leech lattice, with the no-ghost theorem from string theory providing the key constraint. | MATH: Central charge c=24; Monster VOA V^natural with graded dimension ∑_n=−1^∞ dim(V^natural_n) q^n = j(τ)−744 = q^−1+196884q+21493760q^2+…; McKay–Thompson series T_g(τ)=∑ tr(g|V^natural_n)q^n−1 are Hauptmoduln for genus-zero groups; Borcherds' denominator identity for the Monster Lie algebra: e^ρ∏_α∈Δ^+(1−e^−α)^mult(α) = j(σ)−j(τ) (where ρ is the Weyl vector, Δ^+ positive roots of the Monster Lie algebra, and σ,τ are coordinates on the rank-2 hyperbolic lattice). The no-ghost theorem requires the VOA to have c=24 and be self-dual (holomorphic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -