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

TL;DR

The paper establishes a tight link between the chaos bound in boundary CFTs and the Classical Regge Growth (CRG) constraint on the bulk S-matrix in AdS/CFT. By analyzing four-point functions generated by local bulk contact terms in two causal configurations—Regge and causally scattering—the authors express the bulk-point singularity coefficient in terms of the flat-space S-matrix and show that the boundary chaos bound enforces S-matrix growth not exceeding s^2. They generalize Gary’s bulk-point analysis to spinning fields (scalars, gauge bosons, gravitons), demonstrating that the Regge scaling on the causally scattering sheet is governed by the same exponent as on the Regge sheet, thereby tying chaos to CRG for bulk interactions. A detailed a-counting framework connects small-σ and small-ρ expansions, yielding A'≥A and A'≤2, which together imply A≤2 and hence CRG. The results provide strong evidence that holographic boundary theories obey CRG for their bulk duals, with implications for the allowed structure of higher-derivative and spinning interactions in consistent quantum gravity theories.

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 $s^2$ 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.

Figures (17)

• Figure 1: Insertion points in global AdS
• Figure 2: The evolution of $z$ and ${\bar{z}}$ as $\tau$ is decreased from $\pi$ down to $0$ at fixed $\theta$. Note ${\bar{z}}$ touches its maximum value unity at $\tau=\pi -\theta$ and $z$ touches its minimum value, $z=0$ at $\tau=\theta$.
• Figure 3: The evolution of the cross ratio $\sigma$ as $\tau$ is decreased from $\pi$ down to $0$ at fixed $\theta$. Note that $\sigma$ touches its minimum value, $\sigma=0$ at $\tau=\theta$, when $z$ vanishes.
• Figure 4: The evolution of the cross ratio $e^{2 \rho}= \frac{z}{\bar{z}}$ as $\tau$ is decreased from $\pi$ down to $0$ at fixed $\theta$. Note that $e^{2 \rho}$ touches its minimum value, $e^{2 \rho}=0$ at $\tau=\theta$, when $z$ vanishes.
• Figure 5: The path traversed in the complex plane by the variables $z$ (purple) and ${\bar{z}}$ (green) as we lower $\tau$ from $\pi$ to $0$ at fixed $\theta$. The vertical scale in these graphs is greatly exaggerated to make them visible. The actual curves should be thought of as hugging the real axis except in the neighbourhood of the branch points which they circle in the manner shown in this Figure.