UV completion of 2D Ising CFT:a golden E_8 massless $S$-matrix

Abstract

We present a full classification of UV complete QFTs that RG flow to the 2D Ising CFT by solving the bootstrap equations for massless right--left S-matrices. For the Ising model with E_8 spectrum, we find exactly four completions, arising from higher-T\bar T-type deformations, including a previously unknown ``golden flow'' whose UV fixed point is a diagonal su(2) coset CFT (c=25/14) along Δ_{\rm rel}=2/7. A universal Fibonacci/E_8 structure governs the R--L adjacency matrices and the Y-system periods, so that the E_8 symmetry persists across all RG scales.

9 pages, 3 figures