Conformal properties of soft operators: Use of null states

A natural extension of the Pasterski-Shao-Strominger (PSS) prescription is described, enabling the map of Minkowski space amplitudes with massive spinning external legs to the celestial sphere to be performed. An integral representation for the conformal primary wave function (CPW) of massive spinning bosons on the celestial sphere is derived explicitly for spin-one and-two. By analogy with the spin-zero case, the spinning bulk-to-boundary propagator on Euclidean AdS is employed to extend the massive CPW integral representation to arbitrary integer spin, and to describe the appropriate inverse transform of massive spinning CPWs back to the plane wave basis in Minkowski space. Subsequently, a massive spins momentum operator representation on the celestial sphere is determined, and used in conjunction with known Lorentz generators to derive Poincaré symmetry constraints on generic massive spinning two-, three-and four-point celestial amplitude structures. Finally, as a consistency check, three-point Minkowski space amplitudes of two massless scalars and a spin-one or-two massive boson are explicitly mapped to the celestial sphere, and the resulting three-point function coefficients are confirmed to be in exact agreement with the results obtained from Poincaré symmetry constraints.

Section: Introductionmentioning

confidence: 99%

Massive spinning bosons on the celestial sphere

Law

Zlotnikov

2020

“…Celestial diamonds thus offer a natural language for describing the conformally soft sector of celestial CFT and resolve various puzzles surrounding the conformal basis, shadows and helicity degeneracies. They unify the nested primary descendants associated to soft charges found in [36][37][38][39][40][41][42] with the finite dimensional modules of [43] and demonstrate how these relations extend to arbitrary spin. Our wavefunction-based approach provides a bulk picture of what the external scattering states correspond to, a mechanical way to get results guaranteed by representation theory, and lets us decouple what comes from dynamics versus kinematics.…”

Section: Jhep11(2021)072mentioning

confidence: 82%

“…With this mindset, we examine the structure of global conformal multiplets in 2D celestial CFT and perform a classification of all SL(2,C) primary descendants corresponding to massless particles of spin s = 0, 1 2 , 1, 3 2 , 2 . This follows the spirit of [35] from the bootstrap literature, and is inspired by recent work on celestial null states [36][37][38][39][40][41][42][43]. We will see that even the simple case of global conformal multiplets reveals the power of symmetry to organize conformally soft behavior, tying together questions about the vacuum structure of asymptotically flat spacetimes, constraints on celestial amplitudes, and intrinsically 2D descriptions of celestial CFT [44].…”

Section: Jhep11(2021)072mentioning

confidence: 94%

See 1 more Smart Citation

Celestial diamonds: conformal multiplets in celestial CFT

Pasterski¹,

Puhm

Trevisani

2021

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.

“…theorems familiar from Minkowski space amplitudes correspond to so called conformal soft theorems for celestial amplitudes, which were studied in [22][23][24][25][26][27][28][29][30]. The representation of BMS symmetry generators on the celestial sphere, and other aspects such as OPE expansions of celestial operators were discussed in [31][32][33][37][38][39][40].…”

Section: Jhep11(2020)149mentioning

confidence: 99%

Relativistic partial waves for celestial amplitudes

Law

Zlotnikov

2020

The formalism of relativistic partial wave expansion is developed for four-point celestial amplitudes of massless external particles. In particular, relativistic partial waves are found as eigenfunctions to the product representation of celestial Poincaré Casimir operators with appropriate eigenvalues. The requirement of hermiticity of Casimir operators is used to fix the corresponding integral inner product, and orthogonality of the obtained relativistic partial waves is verified explicitly. The completeness relation, as well as the relativistic partial wave expansion follow. Example celestial amplitudes of scalars, gluons, gravitons and open superstring gluons are expanded on the basis of relativistic partial waves for demonstration. A connection with the formulation of relativistic partial waves in the bulk of Minkowski space is made in appendices.