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

Abstract

Abstract We use large spin perturbation theory and the Lorentzian inversion formula to compute order-ϵ corrections to mixed correlators in the O(n) Wilson-Fisher CFT in 4 − ϵ dimensions. In particular, we find the scaling dimensions and averaged OPE coefficients appearing in all correlators involving the operators φ and φ2, for φ2 in both the singlet and symmetric traceless representations of O(n). We extend some computations to the next order, and find order-ϵ2 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.