The five-point bootstrap

Abstract

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators $⟨\sigma \sigma ϵ\sigma \sigma ⟩$ in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff $\Delta ⩽{\Delta }_{\mathrm{cutoff}}$. We then compute several OPE coefficients involving $ϵ$ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

Comments: 24 pages, 1 attached Mathematica notebook, v2: small adjustments, references added, v3: small adjustments, references added, v4: minor error fixed