Shockwaves from the Operator Product Expansion

TL;DR

This paper explores the CFT dual of shockwave geometries in AdS, analyzing operator product expansions in the Regge limit, and clarifies how shockwaves relate to operator insertions and causality constraints in large-N CFTs.

Contribution

It provides a detailed dictionary between shockwave geometries and CFT states, including smearing procedures for light operators and links causality bounds to chaos and bulk conditions.

Findings

The leading OPE contribution in the Regge limit is the shockwave operator.

Smearing light operators projects out double-trace contributions.

Causality constraints in CFT match bulk chaos bounds.

Abstract

We clarify and further explore the CFT dual of shockwave geometries in Anti-de Sitter. The shockwave is dual to a CFT state produced by a heavy local operator inserted at a complex point. It can also be created by light operators, smeared over complex positions. We describe the dictionary in both cases, and compare to various calculations, old and new. In CFT, we analyze the operator product expansion in the Regge limit, and find that the leading contribution is exactly the shockwave operator, $\int du h_{uu}$, localized on a bulk geodesic. For heavy sources this is a simple consequence of conformal invariance, but for light operators it involves a smearing procedure that projects out certain double-trace contributions to the OPE. We revisit causality constraints in large-$N$ CFT from this perspective, and show that the chaos bound in CFT coincides with a bulk condition proposed by Engelhardt and Fischetti. In particular states, this reproduces known constraints on CFT 3-point couplings, and confirms some assumptions about double-trace operators made in previous work.