Having Fun with Theoretical Physics

# Celestial Conformal Colliders

While the ‘soft physics’ investigations have naturally focused on (conformally) soft gauge bosons and gravitons, their collinear limits, and symmetry interpretations, the matter modes that they couple to are equally important. Indeed, Cordova and Shao realized the BMS algebra via light-ray operators constructed from the stress tensor on a fixed light sheet in any unitary (bulk) CFT. Moreover, these matter symmetry generators as well as generalizations of stress tensor light-ray operators featured in conformal collider physics are celestial quasi-primaries! Despite this being mentioned in passing in the seminal work of Hofman-Maldacena, there remains a disconnect between the very rich CFT literature building of this work and the celestial efforts. We are then in a position to fill in this gap. In [2211.14287] we initiated the "celestial conformal colliders" by showing how to extend Cordova-Shao from BMS to w1+∞. As we embark on this initial exploration of celestial conformal colliders, it becomes evident that a rich interplay between various research programs is on the horizon, for instance, the phase space representation of celestial symmetries could be connected to detector operators and consequently infrared-finite amplitudes or event shapes (in the LHC phenomenology community, these are linked to "jet substructure"). Below, we elaborate on some efforts and questions that are poised to drive this intriguing synergy forward.

## Detector Operators for Celestial Symmetries

In [2307.16801], a systematic cataloging of celestial symmetry charges realized in the matter sector of the phase space was presented, which contains a semi-infinite tower of higher-spin light-ray-supported and light-sheet-supported (for the wedge subalgebra) operators.

In particular, considering the w1+∞ symmetry, the first entry of matter charges is precisely the Average Null Energy Condition (ANEC) operator which has been studied extensively in the conformal collider community. The rest tower of matter charges suggests a natural extension of these observables. Moreover, this result informs that celestial symmetries indeed help organize light-ray operators that are of interest in conformal colliders.

## Matter Charges in 4D CFTs

[2211.14287] and [2307.16801] essentially focused on the free 4D CFT. In connection with the conformal collider literature, an intriguing avenue for exploration lies in the explicit computation of the pure matter realizations of the operator algebras in example 4D CFTs. Along these lines, it would also be interesting to further understand the role of the light-sheet-supported operators constructed in [2307.16801] in organizing the scattering observables.

## Higher-spin Generalizations

Our construction [2307.16801] naturally extends to encompass higher-spin symmetries, corresponding to the coupling with higher-spin gauge fields in the bulk. The reason that this direction is worth exploring is two-fold.

Firstly, it raises intriguing questions concerning the nature of these generalized operators. Does this extension yield a closed algebra, and if so, what precisely is the nature of this algebra? Furthermore, how can we comprehend this algebraic structure from the perspective of celestial CFT? These inquiries regarding operator algebra warrant exploration in their own right.

Secondly, the spin-0 generalized operators align with the higher-spin ANEC operators, which offers an additional avenue for advancing the celestial conformal collider framework.