Analytic bootstrap of mixed correlators in the $\mathbf{O}(\mathbf{n})$ CFT

Abstract

We use large spin perturbation theory and the Lorentzian inversion formula to compute order-$\epsilon$ corrections to mixed correlators in the $O(n)$ Wilson-Fisher CFT in $4-\epsilon$ dimensions. In particular, we find the scaling dimensions and averaged OPE coefficients appearing in all correlators involving $\phi$ and ${\phi }^2$, for ${\phi }^2$ in both the singlet and symmetric traceless representations of $O(n)$. We extend some computations to the next order, and find order-${\epsilon }^2$ data for a number of quantities for the Ising case at $n=1$. Along the way, we discuss several interesting technical aspects which arise, including subleading corrections to mixed conformal blocks, projections onto higher twists in the inversion formula, and multiplet recombination.

83pp