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 Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a series of kinks whose locations approach $(\Delta^{\text{Ising}}_{\sigma},\Delta^{\text{Ising}}_{\epsilon})$ at $N\rightarrow \infty$. 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 $\mathcal{W}_3$ algebra saturate the numerical bootstrap bounds of CFTs with $S_3$ symmetry.