Interacting Fields at Spatial Infinity

TL;DR

This paper extends the understanding of massive fields at spatial infinity by providing explicit boundary correlators, a reconstruction formula, and a prescription for meaningful correlators at the blowup of spatial infinity, revealing new decay behaviors and operator bases.

Contribution

It introduces an explicit boundary representation, a reconstruction formula, and an LSZ-like prescription for correlators at spatial infinity, advancing the analysis of interacting massive fields in this regime.

Findings

Interacting massive fields decay slower than free fields near spatial infinity.

A new LSZ-like prescription isolates on-shell correlators at spatial infinity.

Correlators at spatial infinity can be expressed using asymptotic observables.

Abstract

We study the properties of massive fields extrapolated to the blowup of spatial infinity ($\hat{i}^0$), extending the program initiated in arXiv:2207.06406. In the free theory, we find an explicit representation of boundary two-point functions and boundary to bulk two-point functions, and also present an HKLL-type reconstruction formula for local bulk operators in terms of smeared boundary operators. We study interacting Wightman correlators and find that, generically, interacting massive fields decay slower than free fields as one approaches $\hat{i}^0$. We propose that meaningful correlators at $\hat{i}^0$ can be obtained through an LSZ-like prescription that isolates the on-shell part of bulk Wightman correlators before extrapolating them to $\hat{i}^0$. We show that a natural basis for operators at $\hat{i}^0$, defined via this prescription, is given by the average of "in" and "out" operators defined at $i^-$ and $i^+$ respectively. Therefore, correlators at $\hat{i}^0$ and cross correlators between $\hat{i}^0$, $i^-$ and $i^+$ can be represented within the class of asymptotic observables studied by Caron-Huot et al. in arXiv:2308.02125. We present several sample calculations.