Detector Operators for Celestial Symmetries

TL;DR

This paper systematically constructs and extends celestial symmetry generators on phase space, revealing their structure as light-sheet operators and their implications for detector operators at null infinity.

Contribution

It introduces a method to derive celestial symmetry generators from celestial OPEs and extends them beyond the wedge, incorporating linear and higher-particle operators.

Findings

Constructed generators as quadratic light-sheet operators at null infinity.

Extended symmetry algebra beyond the wedge with linear and higher-particle terms.

Provided insights into how celestial symmetries influence detector operator choices.

Abstract

This paper presents a systematic cataloging of the generators of celestial symmetries on phase space. Starting from the celestial OPEs, we first show how to extract a representation of the general-spin analog of the wedge subalgebra of $w_{1+\infty}$ on the phase space of massless matter fields of arbitrary helicity. These generators can be expressed as light-sheet operators that are quadratic in the matter fields at future or past null infinity. We next show how to extend these symmetries beyond the wedge. Doing so requires us to augment the quadratic operators with: 1) linear terms corresponding to primary descendants of the negative helicity gauge fields the matter modes couple to, and 2) a tower of higher-particle composite operator contributions. These modes can be realized as light-ray operators supported on generators of null infinity, but local on the celestial sphere. Finally, we construct a representation of the celestial symmetries that captures how the positive helicity gauge fields transform. We close by discussing how these celestial symmetries inform our choice of detector operators.