Conformal Bootstrap Links Automorphic Spectra, Hyperbolic Geometry, and Gauge Group Detection — E8 Intelligence Research

Abstract

FINDING: Conformal bootstrap uses automorphic spectra and spectral geometry of hyperbolic manifolds to constrain CFT scaling dimensions, with gauge group detection via decoupling operators in d>2. | MATH: Automorphic forms on hyperbolic manifolds ↔ CFT correlation functions; scaling dimensions Δ_i bounded by crossing symmetry and unitarity; decoupling operators encode gauge group (e.g., SU(N)) via null states in OPE. | CONNECTION: D₄ root system (24-cell) appears in 2D CFTs as extended symmetry (e.g., W-algebras) and in higher-dimensional bootstrap as part of exceptional Lie algebra structures; hyperbolic geometry links to modular forms with base-60-like periodicities (e.g., SL(2,Z) action). | DEPTH: 7 — Bridges spectral geometry, number theory, and CFT; provides non-perturbative bounds but no explicit golden ratio or crystallographic constants in the given abstracts. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com