Conformal basis for flat space amplitudes

By Sabrina Pasterski, Shu-Heng Shao. 2017

329 citations recorded by the source corpus.

We study solutions of the Klein-Gordon, Maxwell, and linearized Einstein equations in R1,d+1 that transform as d-dimensional conformal primaries under the Lorentz group SO(1,d+1). Such solutions, called conformal primary wavefunctions, are labeled by a conformal dimension Δ and a point in Rd, rather than an on-shell (d+2)-dimensional momentum. We show that the continuum of scalar conformal primary wavefunctions on the principal continuous series Δ∈d2+iR of SO(1,d+1) spans a complete set of normalizable solutions to the wave equation. In the massless case, with or without spin, the transition from momentum space to conformal primary wavefunctions is implemented by a Mellin transform. As a consequence of this construction, scattering amplitudes in this basis transform covariantly under SO(1,d+1) as d-dimensional conformal correlators.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0fdf1cd2cee5a24c2a091b360d8695aa334c3766

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Citations in the corpus

Lectures on celestial amplitudes (2021, background): “Here it appears as an ambiguity in our choice of basis [18], and can thus play an important role in our celestial dictionary.”
Celestial operator products of gluons and gravitons (2019, unknown): “Celestial amplitudes Ã of massless particles are obtained from momentum-space amplitudes A (including the momentum-conserving delta function) by performing Mellin transformations with respect to the particle energies [5, 12] Ãs1···sn(∆1, z1, z̄1, · · · ,∆n, zn, z̄n) = ( n ∏”
Conformally soft photons and gravitons (2018, methodology): “For this case it was shown [9] that the conformal primary wavefunctions in the unitary principal series with dimensions (32 + iλ 2 ,− 1 2 + iλ 2 ) form a complete basis (for one helicity).”
Bridging Carrollian and celestial holography (2022, background): “Alternatively, as it was pointed out in [68,70] (see [111] for a review), one can express the S-matrix elements in Mellin space using the change of representation discussed in Section 2.”
Asymptotic symmetries and celestial CFT (2020, background): “In this section we review the construction in [16] of conformal primaries in gauge theory and gravity which form a complete conformal basis for single particle states when the spectrum is the principal continuous series of the Lorentz group.”
Bootstrapping inflationary correlators in Mellin space (2019, background): “In this context various new ideas have been set forth recently [133–137] and it would be interesting to further understand the possible relation between the results obtained in this paper and the corresponding flat space analysis which lies in between.”
Gluon Amplitudes as 2d Conformal Correlators (2017, methodology): “ Mellin transforms on inner products of two gauge boson one-particle states. 2 A Conformal Basis for Gauge Bosons In this section we review the massless vector conformal primary wavefunctions in R1;3 [3,10], i.e. solutions to the four-dimensional Maxwell equation that transform as two-dimensional sp”
Soft limits of Yang-Mills amplitudes and conformal correlators (2019, background): “[3, 4].”
Celestial Holography (2021, background): “The Spectrum Finite-energy scattering states, characterized by normalizable single-particle wavepackets in the bulk [15], are captured by celestial operators with a spectrum [97] ∆ = 1 + iλ, λ ∈ R.”
Conformally soft theorem in gauge theory (2019, background): “Recently there has been interest in and explicit construction of amplitudes in a conformal basis on the celestial sphere [1–16], in which the conformal action is trivial but translation invariance is hidden.”
Celestial amplitudes and conformal soft theorems (2019, background): “3 Gravity: ∆ → 0 In [2], it was shown that graviton conformal primaries with ∆ = 0 are also pure gauge.”