Scalar CFTs and their large N limits

Abstract

We study scalar conformal field theories whose large N spectrum is fixed by the operator dimensions of either the Ising model or the Lee-Yang edge singularity. Using the numerical bootstrap to study CFTs with SN ⊗ Z2 symmetry, we find a series of kinks whose locations approach (ΔσIsing, Δ∈Ising) at N → ∞. Setting N = 4, we study the cubic anisotropic fixed point with three spin components. As byproducts of our numerical bootstrap work, we discover another series of kinks whose identification with previous known CFTs remains a mystery. We also show that “minimal models” of W3 algebra saturate the numerical bootstrap bounds of CFTs with S3 symmetry.