Celestial conformal colliders

Abstract

We start by observing that the light-ray operators featured in the conformal collider literature are celestial primaries. This allows us to rephrase the corresponding 4D CFT correlators as probing a conformally soft matter sector of the 2D celestial CFT (CCFT). To demonstrate the utility of this perspective we show how the recent w1+∞ symmetry observed in CCFT suggests a natural extension of the conformal collider operators.

Equating extrapolate dictionaries for massless scattering

“…This could be applied either to construct an 𝑆-matrix like object for a 4D CFT or to describe perturbative amplitudes more generally, for the case where the 4D CFT is the free theory. On the one hand these manipulations are convenient for understanding celestial OPEs and adopting technology and results already developed in the conformal collider literature [60,61] to the celestial hologram [62,63]. Meanwhile we see how the extrapolate dictionary gets modified when the bulk scaling dimension runs, which is relevant to the weakly coupled detector story [54] and provides some insight into how this modification to the expected radiative falloffs would affect what we mean by the scattering data.…”

“…20 However, other choices of conformal frame are more convenient for understanding the OPEs of celestial operators. In this appendix we will look at a particular example where we map null infinity to a null hyperplane within a single Poincaré patch (exchanging the origin and the 𝑢 = 𝑧 = z = 0 point on the celestial sphere) studied by Hoffman and Maldacena [60] and used for examining the appearance of BMS symmetries in generic unitary 4D CFTs by Cordova and Shao [61] (see also [62,63]).…”

“…where 𝑋 ± = 𝑋 0 ±𝑋 3 and similarly 𝑌 ± = 𝑌 0 ±𝑌 3 . It finds applications in the construction of detector operators for conformal collider physics [60] as well as their celestial generalizations [62].…”

On infinite symmetry algebras in Yang-Mills theory

“…The relevance of the cubic component of the symmetry charge for the quadratic order w 1`8 algebra for spin-2 charges in the matter sector was already pointed out in [11]. We are also aware of a forthcoming paper [12] which presents complementary results on higher-helicity fields.…”

A comment on loop corrections to the celestial stress tensor

“…The position space picture of massless scattering in terms of correlation functions of operators at null infinity lends itself to identifying intrinsically defined Carrollian field theory duals living at null infinity [32]. Moreover, the manner in which the celestial operators are smeared along null infinity matches certain light ray operators common in the CFT literature, restricted to a light sheet in 4D [33]. In the perturbative limit, these light ray operators further connect to phase space realizations of the celestial symmetry algebras [34].…”