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

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.

Notes on flat-space limit of AdS/CFT

“…It is also of great importance to derive complete formulas of flat-space limit for spinning correlators, or at least do more examples at four-point level in terms of Mellin space, coordinate space or partial-wave expansion, see e.g., [68,69] for recent nice trying. This could shed light on color-kinematic duality and double-copy relation (see [70,71]) in CFT (see [72][73][74][75] for insightful studies in momentum space of AdS/CFT).…”

Sharp boundaries for the swampland

“…2 At leading order for large N , the bound on the Regge behavior of the CFT correlator is known as the chaos bound [24]. The chaos bound translates precisely to the O(s 2 ) bound of the Classical Regge Growth conjecture, as has been carefully argued in the recent paper [19]. It would be very interesting to see whether the arguments of [19] can be extended to the nonperturbative regime and give a rigorous justification for our assumption that the Regge growth is strictly better than O(s 2 ).…”

“…We will in particular assume that the same Regge bound lim s→∞ M(s, u)/s 2 = 0 (for fixed u < 0) holds also in this case. Note that this is a little stronger than the O(s 2 ) bound assumed in the "Classical Regge Growth" conjecture [17][18][19], which is believed to hold for any consistent tree-level S-matrix; we need to require that at the nonperturbative level the Regge growth is strictly smaller than s 2 . The best heuristic justification for such a behavior comes from physical arguments that the scattering amplitude in impact parameter space should be analytic and bounded, as a consequence of unitarity and causality.…”

Causality constraints in Quadratic Gravity

“…Our result indicates that Quadratic Gravity is better behaved than naively expected and, thus, it may contribute towards the finer classification of consistent gravitational theories, where we need to impose restrictions on four-point (or higher) couplings in addition to the causality constraints. One such constraint is the CRG bound as depicted in [4,5].…”

“…Since the set of all such terms is infinite-dimensional, this requirement appears to set a Herculean task. However, in a pair of interesting papers [4,5], the authors not only classified all such higher derivative terms but also defined a set of consistency constraints dubbed as classical Regge growth (CRG). Using these constraints, they proved that in D ≤ 6, GR is the only consistent theory.…”