Scalar CFTs and their large N limits

Abstract

A bstract 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 S N ⊗ Z 2 symmetry, we find a series of kinks whose locations approach (Δ σ Ising , 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 $$ {\mathcal{W}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> algebra saturate the numerical bootstrap bounds of CFTs with S 3 symmetry.