“Moments and saddles of heavy CFT correlators”
In conformal field theory, four-point functions of scalar operators with large scaling dimension ∆ describe scattering of massive states (m ∼ ∆) in the ambient AdS spacetime. Understanding these scattering processes is vital for probing many-body physics with gravitational interactions and exploring the bulk dynamics of heavy objects, such as black holes.
In weakly coupled bulk theories, ϕN particle jets scatter through distinct multi-particle exchanges, encoded by decomposing the correlation function into deformed higher-spin conformal blocks. At large ∆ϕ, these structures coalesce into Gaussian “saddles” in the ϕN × ϕN OPE, and are governed by a small number of moment variables. Leveraging fractional calculus, we study the OPE as a Stieltjes moment problem and use analytic bootstrap techniques to establish bounds on moment sequences in the heavy limit. These results uncover novel constraints on the statistics of CFT data and suggest new frameworks for understanding heavy correlators in strongly interacting theories.
Host: David Poland