4D scattering amplitudes and asymptotic symmetries from 2D CFT
Abstract
We 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.
Additional Information
© 2017 The Author(s). Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. C.C. is supported by a Sloan Research Fellowship and a DOE Early Career Award under Grant No. DE-SC0010255. A.D. and R.S. are supported in part by the NSF under Grant No. PHY-1315155 and by the Maryland Center for Fundamental Physics. R.S. would also like to thank the Gordon and Betty Moore Foundation for the award of a Moore Distinguished Scholar Fellowship to visit Caltech, as well as the hospitality of the Walter Burke Institute for Theoretical Physics, where a substantial part of this work was completed. The authors are grateful to Nima Arkani-Hamed, Ricardo Caldeira Costa, Liam Fitzpatrick, Ted Jacobson, Dan Kapec, Jared Kaplan, Juan Maldacena, Ira Rothstein, and Anthony Speranza for useful discussions and comments.Attached Files
Published - art_3A10.1007_2FJHEP01_282017_29112.pdf
Submitted - 1609.00732.pdf
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Additional details
- Eprint ID
- 76653
- Resolver ID
- CaltechAUTHORS:20170419-075551109
- Alfred P. Sloan Foundation
- Department of Energy (DOE)
- DE-SC0010255
- NSF
- PHY-1315155
- Maryland Center for Fundamental Physics
- Gordon and Betty Moore Foundation
- Walter Burke Institute for Theoretical Physics, Caltech
- Created
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2017-04-19Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics