Negative shocks versus static patch holography
arXiv:2607.14042
The paper investigates a conjecture that the Euclidean gravitational path integral, including an observer worldline, computes a trace in de Sitter static‑patch holography, testing it via two‑point functions and out‑of‑time‑ordered correlators and finding violations of trace cyclicity and positivity.
Abstract
We study a version of de Sitter static patch holography in which the Euclidean gravitational path integral, with an observer worldline included, is conjectured to compute a trace. Motivated by recent evidence for this conjecture from the sphere path integral, we test it further by inserting operators along the observer worldline and computing two-point functions and out-of-time-ordered four-point correlators (OTOCs). We extend an earlier OTOC calculation by Kolchmeyer and Liu using the shockwave formalism, incorporating both observer recoil and gravitational backreaction. We find that the OTOC conflicts with two basic properties of a trace in a Hilbert space: cyclicity and positivity. The signaling feature of the shockwave geometry gives rise to two distinct resummations of the perturbative eikonal expansion, which are interchanged by cyclicity. Positivity is violated by the fact that the leading perturbative contribution causes the (regularized) OTOC to increase.
30 pages plus appendices