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Asymptotic symmetries and celestial CFT

Authors
  • Donnay, Laura1, 2, 2
  • Pasterski, Sabrina3, 2
  • Puhm, Andrea4, 2, 2
  • 1 Vienna University of Technology, Vienna, A-1040, Austria , Vienna (Austria)
  • 2 Harvard University, Cambridge, MA, 02138, USA , Cambridge (United States)
  • 3 Princeton Center for Theoretical Science, Princeton, NJ, 08544, USA , Princeton (United States)
  • 4 CPHT, CNRS, Ecole polytechnique, IP Paris, Palaiseau, F-91128, France , Palaiseau (France)
Type
Published Article
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Publication Date
Sep 28, 2020
Volume
2020
Issue
9
Identifiers
DOI: 10.1007/JHEP09(2020)176
Source
Springer Nature
Keywords
License
Green

Abstract

We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension ∆. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series ∆ ∈ 1 + iℝ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S2) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.

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