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We study four-point functions of scalars, conserved currents, and stresstensors in a conformal field theory, generated by a local contact term in thebulk dual description, in two different causal configurations. The first ofthese is the standard Regge configuration in which the chaos bound applies. Thesecond is the `causally scattering configuration' in which the correlatordevelops a bulk point singularity. We find an expression for the coefficient ofthe bulk point singularity in terms of the bulk S matrix of the bulk dualmetric, gauge fields and scalars, and use it to determine the Regge scaling ofthe correlator on the causally scattering sheet in terms of the Regge growth ofthis S matrix. We then demonstrate that the Regge scaling on this sheet isgoverned by the same power as in the standard Regge configuration, and so isconstrained by the chaos bound, which turns out to be violated unless the bulkflat space S matrix grows no faster than $s^2$ in the Regge limit. It followsthat in the context of the AdS/CFT correspondence, the chaos bound applied tothe boundary field theory implies that the S matrices of the dual bulk scalars,gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.

Bounds on Regge growth of flat space scattering from bounds on chaos