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} = 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).
Highlights
In this work, we study a product of null-integrated operators on the same null plane in a conformal field theory (CFT) in d > 2 dimensions: ∞dv1 O1;v···v(u = 0, v1, y1)dv2 O2;v···v(u = 0, v2, y2). −∞ (1.1)Here, we use lightcone coordinates ds2 = −du dv + y2, y ∈ Rd−2. (1.2)The operators are located at different transverse positions y1, y2 ∈ Rd−2, and their spin indices are aligned with the direction of integration
The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula
We study a product of null-integrated operators on the same null plane in a conformal field theory (CFT) in d > 2 dimensions:
Summary
We study a product of null-integrated operators on the same null plane in a conformal field theory (CFT) in d > 2 dimensions (figure 1):. Each null-integrated operator is pointlike in the transverse plane Rd−2, so it is natural to ask whether there exists an operator product expansion (OPE) describing the behavior of the product (1.1) at small |y12|:. We focus on contributions to the OPE with low spin in the transverse d − 2-dimensional space (defined in more detail below).2 These contributions are given by operators O±i,J with spin J =. In equation (1.7), the representation λ is restricted to traceless-symmetric transverse spins that can appear in the conventional OPE of local operators Tμν × Tρσ. These are the representations λ ∈ {, , , ,. They arise in commutators of null-integrated operators [10], leading to an interesting algebra
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