Defect McKay-Thompson Series and Genus-Zero Monstrous Moonshine — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Defect McKay-Thompson series for the Monster CFT generalize the genus-zero property of Monstrous Moonshine to twined partition functions with line defects inserted. | MATH: T_g(q) = Σ tr(g|V_n) q^n forms Hauptmoduln for genus-zero subgroups Γ_g ⊂ SL(2,ℝ); Lin–Shao (2021) construct defect-twined analogues T_{g,D}(q) where D is a topological line defect, conjecturally also Hauptmoduln. Modular invariance group of the defect theory constrains the series. | CONNECTION: Genus-zero condition ↔ modular curve X(Γ_g) has genus 0 ↔ rational parametrization by a single Hauptmodul; the Monster's 194 conjugacy classes map to 171 distinct genus-zero groups (Thompson). Moonshine coefficients encode dimensions of Monster irreps: 196884 = 196883 + 1, where 196883 is the smallest nontrivial Monster irrep dimension. These integers relate to the Leech lattice (24-dim even unimodular, no roots) and its automorphism group Co_0 → Monster. | DEPTH: 9
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**1. Key mathematical insight**
The 1992 Mo
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026defect,
title = {{Defect McKay-Thompson Series and Genus-Zero Monstrous Moonshine — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658586},
url = {https://zenodo.org/records/23658586},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Defect McKay-Thompson Series and Genus-Zero Monstrous Moonshine — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658586
UR - https://zenodo.org/records/23658586
AB - FINDING: Defect McKay-Thompson series for the Monster CFT generalize the genus-zero property of Monstrous Moonshine to twined partition functions with line defects inserted. | MATH: T_g(q) = Σ tr(g|V_n) q^n forms Hauptmoduln for genus-zero subgroups Γ_g ⊂ SL(2,ℝ); Lin–Shao (2021) construct defect-twined analogues T_{g,D}(q) where D is a topological line defect, conjecturally also Hauptmoduln. Modular invariance group of the defect theory constrains the series. | CONNECTION: Genus-zero condition ↔ modular curve X(Γ_g) has genus 0 ↔ rational parametrization by a single Hauptmodul; the Monster's 194 conjugacy classes map to 171 distinct genus-zero groups (Thompson). Moonshine coefficients encode dimensions of Monster irreps: 196884 = 196883 + 1, where 196883 is the smallest nontrivial Monster irrep dimension. These integers relate to the Leech lattice (24-dim even unimodular, no roots) and its automorphism group Co_0 → Monster. | DEPTH: 9 --- **1. Key mathematical insight** The 1992 Mo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -