4D scattering amplitudes and asymptotic symmetries from 2D CFT

By C. Cheung, A. Fuente, R. Sundrum. 2016

287 citations recorded by the source corpus.

A bstractWe reformulate the scattering amplitudes of 4D flat space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors of 4D gauge theory and gravity. Consistent with the topological nature of Chern-Simons theory, Aharonov-Bohm effects record the “tracks” of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories. Soft particle exchanges between hard processes define the Kac-Moody level and Virasoro central charge, which are thereby related to the 4D gauge coupling and gravitational strength in units of an infrared cutoff. Finally, we discuss a toy model for black hole horizons via a restriction to the Rindler region.

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

View Paper: https://www.semanticscholar.org/paper/6b30a4dbfc3e615e341d86e24d1fd2b57f3b24c3

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Citations in the corpus

Conformal basis for flat space amplitudes (2017, methodology): “The same conclusion was reached from studying the AdS holography on each hyperbolic slice of Minkowski space [3, 4].”
Gluon Amplitudes as 2d Conformal Correlators (2017, methodology): “We will restrict ourselves to four-dimensional Minkowski space R1,3 with spacetime coordinates Xµ (µ = 0, 1, 2, 3).”
Lectures on celestial amplitudes (2021, methodology): “A similar route was followed by [23] which nicely demonstrated features of the IR symmetry currents from this slicing point of view.”
Unifying relations for scattering amplitudes (2017, background): “This is of particular interest given the central role of the soft graviton as the stress tensor for a CFT whose correlators are flat space scattering amplitudes [36, 37].”
The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “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”
Flat holography: aspects of the dual field theory (2016, result): “This rather simple analysis, based on the highest weight representations of the BMS4 algebra, is reminiscent of some recent work [10, 16, 17] where bulk physics of 4d asymptotically Minkowski spacetime was recovered from 2d CFTs.”
Celestial operator products of gluons and gravitons (2019, unknown): “Celestial operator spectra were studied in [4–11] and celestial scattering amplitudes in [12–25].”
Lectures on the Infrared Structure of Gravity and Gauge Theory (2017, background): “There is even an operator constructed from soft gravitons [67, 68, 117] whose Ward identities are those of a two-dimensional stress tensor.”
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.”
Superrotation charge and supertranslation hair on black holes (2016, background): “Some recent progress has appeared in [97, 98].”
Celestial Holography (2021, background): “Determining the precise phrasing of these statements within the CCFT framework is an active area of research [98, 206, 207] which will help bridge the gap between the celestial holography program and standard techniques from AdS holography for quantum information exchange.”
Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere (2016, unknown): “In [8] one contribution to such amplitudes (from the interior of the forward lightcone) was expressed as a Witten diagram, but to obtain the full amplitude additional harder-to-compute contributions (from outside the lightcone) must be added in.”
Celestial amplitudes and conformal soft theorems (2019, methodology): “limit. This ∆ = 2 pure diﬀeomorphism state can be used to construct a stress tensor for a boundary CFT on S2 whose insertion into a correlator leads to the sub-leading energetic soft graviton theorem [7, 8]. In the context of celestial scattering, (A.12) indicates that ∆ → 2 will be linked with a co”