Analytic bootstrap of mixed correlators in the O(n) CFT

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 the operators 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.

Automated summary

This study utilizes 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. It determines the scaling dimensions and averaged OPE coefficients for correlators involving the operators phi and phi(2), including both the singlet and symmetric traceless representations of O(n). The study also discusses various technical aspects such as subleading corrections to mixed conformal blocks, projections onto higher twists in the inversion formula, and multiplet recombination.