Analytic Euclidean Bootstrap

Understand

We solve crossing equations analytically in the deep Euclidean regime.

• Large scaling dimension $\Delta$ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the other channel.
• Subleading $1\over \Delta$ tails are systematically captured by including more operators in the Euclidean OPE in the dual channel.
• We use dispersion relations for conformal partial waves in the complex $\Delta$ plane, the Lorentzian inversion formula and complex tauberian theorems to derive this result.