Celestial diamonds: conformal multiplets in celestial CFT

Abstract

We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} $$ 0 1 2 1 3 2 2 we classify and construct all SL(2,ℂ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,ℂ) conformal dimension ∆ and spin J. Radiative conformal primary wavefunctions have J = ±s and give rise to conformally soft theorems for special values of ∆ ∈ $$ \frac{1}{2}\mathbb{Z} $$ 1 2 ℤ . They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have |J| ≤ s. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

Conformally soft fermions

“…Because their existence is tied to supersymmetry [50,51] and double copy relations [50,53] which connect fields of lower spin to those with large gauge symmetries, we expect them to play an important role in understanding the analog of the spin shifting amplitudes relations within celestial CFT. Indeed, we see that these fermionic and bosonic diamonds glue together into a celestial pyramid, which nicely unites the spin-shifting analysis of [50] and conformal multiplet studies of [37,38].…”

“…[33][34][35][36]. In the conformal basis, all of these modes are nicely captured by celestial diamonds [37,38].…”

“…Generalized conformal primary wavefunctions. Generalized bulk wavefunctions for half-integer spins s ≤ |J| were discussed in [37,50]. We focus here on the analytic wavefunctions built from the generalized scalar ϕ gen ∆ = f (X 2 )ϕ ∆ .…”

“…Enforcing the chiral projection of the Rarita-Schwinger equation ε µνρκ σν ∇ ρ χ gen ∆,J;κ = 0 as well as the gauge conditions ∇ µ χ gen ∆,J;µ = 0 , X µ χ gen ∆,J;µ = 0 , σµ χ gen ∆,J;µ = 0 , (2.15) yields the radiative conformal primary wavefunctions (2.9) and their shadows (2.11) for generic ∆ ∈ C and J = ± 3 2 , as well as a discrete set of solutions ∆ = 5 2 and J = ± 1 2 which we will come back to in section 4. 2 We have chosen the normalization conventions of [37] which differ from those of [4,50] by an overall sign in the s = 1 2 shadow wavefunctions.…”

“…For special values of the conformal dimension celestial primary operators will have SL(2, C) primary descendants [39][40][41]. Celestial diamonds [37,38] provide a celestial CFT interpretation for the structure of these conformal multiplets. As observed in [37], this structure persists beyond the conformally soft theorems with asymptotic symmetry interpretations, capturing both the most subleading soft theorems, as well as the infinite towers of primaries giving symmetry enhancements in the single helicity sector [9,42].…”