Squinting at massive fields from infinity

TL;DR

This paper introduces a new asymptotic limit for massive scalar fields in flat spacetime, enabling boundary reconstruction of bulk operators via smearing functions, and explores the boundary algebra's properties in free and interacting theories.

Contribution

It develops a novel boundary limit for massive fields in flat space, allowing bulk-boundary reconstruction and analysis of boundary algebra in quantum field theories.

Findings

Boundary limit yields boundary dS$_3$ with exponential tail suppression.

Bulk operators can be reconstructed from boundary data using smearing functions.

The procedure remains well-defined with interactions, as shown by perturbation theory.

Abstract

We study a novel asymptotic limit of massive scalar fields in nongravitational quantum field theories in four-dimensional flat space. We foliate the spacetime into a set of dS$_3$ slices that are spacelike to, and at a constant proper distance from, an arbitrarily chosen origin, and study the boundary dS$_3$ obtained in the infinite-distance limit. Massive bulk fields have an exponentially small tail in this limit, and by stripping off this tail we obtain observables that are intrinsic to the boundary dS$_3$. A single massive field in the bulk can be decomposed into an infinite set of dS$_3$ fields, and the Minkowski vacuum corresponds to the Euclidean vacuum for these fields. Our procedure for extrapolating bulk observables induces potential singularities in boundary correlators but we show how they can be cured in the free theory by smearing the boundary operators. We show that by integrating boundary operators with suitable smearing functions it is possible to reconstruct all local bulk operators in the free theory. We argue, using perturbation theory, that our extrapolation procedure continues to be well defined in the presence of interactions. We demonstrate a relationship between the width of the boundary smearing function and the localization of the bulk field. We study other interesting properties of the boundary algebra including the action of global translations and the manner in which local bulk interactions are encoded on the boundary.