Abstract
We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the ‘causally scattering configuration’ in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than s2 in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.
Highlights
It has recently been conjectured that the tree level S matrix of any ‘consistent’1 classical theory never grows faster with s than s2 in the Regge limit
We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations
We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix
Summary
It has recently been conjectured that the tree level S matrix of any ‘consistent’ classical theory never grows faster with s than s2 in the Regge limit. In this paper we demonstrate that the four-point function generated holographically by a local bulk contact term for scalars, gauge fields, or the metric necessarily violates the chaos bound whenever the flat space S matrix generated by the same contact term violates the CRG conjecture. As the insertion parameters θ and τ run over the range of study (2.2), the conformal cross ratios σ and ρ (or equivalently z and z -see around (2.6) for definitions) range over three different sheets in the complex cross ratio space corresponding to three distinct causal configurations (2.3) of the boundary points. Recall that the chaos bound theorem of [1] implies (see the appendix of that paper and section 6 for a brief review) that the correlator for a well behaved (unitary etc) boundary theory cannot grow faster than 1 σ in the small σ limit on the causally. The chaos bound applied to boundary correlators of a unitary theory implies that the bulk dual of that theory obeys the CRG conjecture
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