Conformal blocks from celestial gluon amplitudes

Abstract

In celestial conformal field theory, gluons are represented by primary fields with dimensions ∆ = 1 + iλ, λ ∈ ℝ and spin J = ±1, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are “compatible” in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions ∆ = 2 + M + iλ, where M ≥ 0 is an integer, with integer spin J = −M, −M + 2, …, M − 2, M. They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions.

Revisiting the conformally soft sector with celestial diamonds

“…In the bulk we know that they are symplectic partners and inherit Hermiticity conditions from the reality of the gauge field and metric. This might hint at a single dual field, however our understanding of the 2D Hilbert space is still evolving[62,63] 21. The JL are polynomial in w. In the recent investigations[64,65] the coefficients of these polynomials are shown to obey interesting symmetry algebras.…”

Celestial diamonds: conformal multiplets in celestial CFT

“…A final observation is that it is possible to mimic radial quantization also in celestial CFTs (see e.g. the discussion of [17]). Indeed, since the inner product (3.19) is delta normalized, we can obtain a two-point function power-like behavior by taking a 2D shadow transform of the out states.…”

“…(C.21) 17 We will modify our notation to avoid confusion with the Poincaré generators that appear elsewhere in this paper as well as the representation of this algebra in celestial amplitudes in [11,15].…”

“…This paradigm puts the symmetries of the theory front and center. Recognizing [1,2] that the asymptotic symmetry group of the theory [3,4] is hidden in IR divergences and factorization theorems [5] in typical presentations of scattering amplitudes has led to a fascinating convergence of tools from the relativity [6][7][8] and amplitudes [9][10][11][12][13][14][15][16][17][18][19] communities. 1 While the S-matrix can be used to diagnose the physical relevance of a proposed symmetry extension, geometric tools have the power to provide general statements that would be difficult to extract from perturbation theory.…”

State-operator correspondence in celestial conformal field theory

“…Shadowing one of the primary fields in the two-point function transforms the delta function to the more familiar CFT 2 power law. Shadows have been ubiquitous in discussions of CCFT, 1 indeed in [16] the scattering of shadow states was recently derived and found to have elegant factorization properties.…”