The light-ray OPE and conformal colliders

TL;DR

This work establishes a nonperturbative, convergent OPE for products of null-integrated operators on a common null plane in any d>2 CFT, decomposing them into light-ray operators computed via a generalized Lorentzian inversion formula. It introduces celestial blocks as the natural nonperturbative building blocks for event shapes and demonstrates a celestial-block expansion for energy-energy correlators, validated nonperturbatively in N=4 SYM across weak to strong coupling and extended to four loops. The formalism clarifies commutativity constraints, uncovers superconvergence relations in nu-space, and provides a robust framework for extracting and constraining OPE data from event shapes through both celestial and t-channel perspectives. The results yield concrete predictions for EEC in N=4 SYM at high loop orders and offer a versatile, nonperturbative toolkit for studying event shapes in conformal and holographic contexts, with broad potential applications to QCD-like theories and gravitational scattering.

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 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).

Figures (14)

• Figure 1: The local operators $\mathcal{O}_1$ and $\mathcal{O}_2$ are integrated along parallel null lines (blue) on the same null plane. On the left, we show a conformal frame where the null plane is $u=0$, and the operators are at different transverse positions $\vec{y}_1,\vec{y}_2\in \mathbb{R}^{d-2}$. On the right, we show a conformal frame where the null plane is future null infinity $\mathscr{I}^+$ and the null-integrated operators are separated by an angle $\theta_{12}$ on the celestial sphere. We give the relationship between $\theta_{12}$ and $\vec{y}_{12}$ in (\ref{['eq:zetacrossratio']}). Note that the entire circle at spatial infinity is really a single point $i^0$. Thus, the operators become coincident at the beginnings and ends of their integration contours.
• Figure 2: Chew-Frautschi plot of neutral even-spin operators. Local operators are denoted by black dots, gray dots denote shadow operators. Solid lines represent Regge trajectories. The low transverse spin terms in the OPE $\int dv T_{vv}\times\int dv T_{vv}$ are spin-3 light-ray operators on even-spin Regge trajectories, shown here by red crosses.
• Figure 3: Minkowski patch $\mathcal{M}_d$ (blue, shaded) inside the Lorentzian cylinder $\widetilde{\mathcal{M}}_d$ in the case of 2 dimensions. Spacelike infinity of $\mathcal{M}_d$ is marked by $i^0$ and future/past infinity are marked by $i^\pm$. The dashed lines should be identified. The point $\mathcal{T} p$ is obtained from $p$ by shooting light-rays in all possible future directions (dotted lines) and finding the first point where they converge.
• Figure 4: A one-point event shape Akiyama:2019cqa. The detector $\mathcal{O}=\mathcal{O}_\mathrm{EHT}$ is integrated along a null line (blue) along future null infinity, starting at spatial infinity $i^0$ and ending at future timelike infinity $i^+$. (Note that the circle at spatial infinity is really a single point.) The red wavy lines indicate energy propagating from the interior of Minkowski space out to null infinity, created by the insertion of the source $\phi_1(p)$.
• Figure 5: The causal relationship between points $2>3>1^-$ used in (\ref{['eq:lighttransformsimplekinematics']}). The lightcone of $2$ is drawn in gray and the lightcone of $1$ in purple.