The light-ray OPE and conformal colliders

Abstract

We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. For example, a product of average null energy (ANEC) operators has an expansion in the light-ray operators that appear in the stress-tensor OPE. An important application is to collider event shapes. The light-ray OPE gives a nonperturbative expansion for event shapes in special functions that we call celestial blocks. As an example, we apply the celestial block expansion to energy-energy correlators in $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. Using known OPE data, we find perfect agreement with previous results both at weak and strong coupling, and make new predictions at weak coupling through 4 loops (NNNLO).

Bounds on Regge growth of flat space scattering from bounds on chaos

“…It follows from the analysis of appendix B.4 27 that the lightcones that emanate out of these four points have no common intersection for τ = 0. 28 When τ = 0, on the other hand (i.e. at the edge of the parameter range (2.2), i.e.the limit (2.8) in which ρ → 0) 29 the vectors P 1 , P 2 , P 3 and P 4 are linearly dependent.…”

“…30 27 In the language Appendx B.4(2.1) is a Case 1 configuration of boundary points withQ = 4. 28 In this generic situation the subalgebra of the conformal algebra that stabilizes the collection of points P1, P2, P3 and P4 -and so the vector space R 2,2 of embedding space vectors spanned by P1 . .…”

Light-ray operators, detectors and gravitational event shapes

“…14 Spaces that admit expansions of the form (5.2) are called Christodoulou-Klainerman (CK) spaces in the literature [110,111]. Physically, the shear tensor encodes gravitational radiation analogously to Maxwell field strength 15…”

“…Moreover, the connection between energy event shapes and the ANEC operator establishes bounds on the a and c coefficients characterizing the conformal anomaly [9,12,13]. Of course, such developments led to increased interest in CFT light-ray operators which culminated in the systematic analysis of [14][15][16][17].…”

Dispersion formulas in QFTs, CFTs and holography

“…Event shapes of light-ray operators are simplest to compute in momentum eigenstates and can be used to derive bounds on the CFT data. For example, positivity of one-point energy correlators gives the well-known conformal collider bounds [128] while two-point event shapes lead to superconvergent sum rules [129,130]. There is also a direct connection between two-point event shapes, analytic functionals, and the CFT dispersion formula [99].…”