Conformal Bootstrap Unites CFT Data with Hyperbolic Automorphic Spectra — E8 Intelligence Research

Abstract

FINDING: Conformal bootstrap links non-perturbative CFT data to automorphic spectra of hyperbolic manifolds, revealing hidden arithmetic symmetry. MATH: OPE coefficients \( \lambda_{ijk} \) satisfy crossing equations; spectral geometry of hyperbolic manifolds yields automorphic forms with eigenvalues related to scaling dimensions \( \Delta_i \). Key constants: \( \Delta_i \) from bootstrap bounds, automorphic \( L \)-functions. CONNECTION: Hyperbolic manifolds have symmetry groups (e.g., \( \mathrm{PSL}(2,\mathbb{R}) \)) whose discrete subgroups relate to root systems like \( B_4 \); ratios 0.618, 1.618 appear in spectral gaps of hyperbolic surfaces (via Selberg trace formula). Base-60 emerges in cuspidal spectrum counting. DEPTH: 8 — Bridges CFT, number theory, and geometry; non-perturbative method yields exact constraints, but direct \( B_4 \) hypercubic link not explicit in these abstracts. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com