Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere

By Sabrina Pasterski, Shu-Heng Shao, Andrew Strominger. 2016

381 citations recorded by the source corpus.

The four-dimensional (4D) Lorentz group $SL(2,\mathbb{C})$ acts as the two-dimensional (2D) global conformal group on the celestial sphere at infinity where asymptotic 4D scattering states are specified. Consequent similarities of 4D flat space amplitudes and 2D correlators on the conformal sphere are obscured by the fact that the former are usually expressed in terms of asymptotic wavefunctions which transform simply under spacetime translations rather than the Lorentz $SL(2,\mathbb{C})$. In this paper we construct on-shell massive scalar wavefunctions in 4D Minkowski space that transform as $SL(2,\mathbb{C})$ conformal primaries. Scattering amplitudes of these wavefunctions are $SL(2,\mathbb{C})$ covariant by construction. For certain mass relations, we show explicitly that their three-point amplitude reduces to the known unique form of a 2D CFT primary three-point function and compute the coefficient. The computation proceeds naturally via Witten-like diagrams on a hyperbolic slicing of Minkowski space and has a holographic flavor.

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

View Paper: https://www.semanticscholar.org/paper/3eb368b4c5c02e38c4a17490ea263455a18dd8a8

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Citations in the corpus

Conformal basis for flat space amplitudes (2017, methodology): “Let us review the massive scalar conformal primary wavefunction defined in [5].”
Infrared Divergences in QED, Revisited (2017, neutral): “(9)There may be a preferred Lorentz covariant dressing if the charged particles are taken as conformal primaries rather than plane waves as in [26].”
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.”
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): “Recently, it was noted that there is another basis which represents massless spin s free fields in d + 2 dimensional Minkowski space as spin s conformal primaries on the d-sphere [1–3].”
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.”
The Holographic Nature of Null Infinity (2020, background): “There has been considerable work on understanding holography in asymptotically flat spacetimes starting with the work of de Boer and Solodukhin [8, 9, 10, 11, 12, 13, 14].”
Lessons from the information paradox (2020, background): “This is just part of a broader program of understanding how holography works in flat space, including the question of how asymptotic symmetries constrain asymptotic correlators and other physical quantities [95–101] on which there is significant literature starting with the work of de Boer and Solod”
Lectures on the Infrared Structure of Gravity and Gauge Theory (2017, background): “Of course, this Green’s function seems quite special since it does not depend on τ at all, but in other applications to flat space holography [142,143], H3 Green’s functions (or bulk-to-boundary propagators) for fields of any conformal weight can arise and are accompanied by τ -dependence in the ful”
Asymptotic symmetries and celestial CFT (2020, background): “This provoked reexamining scattering amplitudes in a basis [15–17] that makes conformal covariance manifest which, in turn, demanded a new understanding of the conformal analog of soft theorems [18–27].”
The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, neutral): “Indeed, even some first hints for such a description, seen in perturbation theory, involve much more alien combinatorial, geometric and number-theoretic ideas [9–16], from which the physics of spacetime and quantum mechanics—locality and unitarity—emerge as derivative notions, with a huge amount lef”
Lectures on celestial amplitudes (2021, methodology): “Similar integral transforms exist for the massive case which are built using tools from the CFT embedding space formalism applied to the p(2) = m(2) hyperboloid [16].”
Celestial operator products of gluons and gravitons (2019, positive): “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 ∏”
Gluon Amplitudes as 2d Conformal Correlators (2017, background): “In [10] (see also [25,28] for the scalar case) the inner product between four-dimensional oneparticle states of spin one was computed in the space of conformal primary wavefunctions.”