A discrete basis for celestial holography

• Published in: The journal of high energy physics Vol. 2024; no. 2; pp. 176 - 53
• Main Authors: Freidel, Laurent, Pranzetti, Daniele, Raclariu, Ana-Maria
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 23.02.2024; Springer Nature B.V; SpringerOpen
• Subjects: Celestial sphere; Classical and Quantum Gravitation; Classical Theories of Gravity; Conformal and W Symmetry; Eigenvectors; Elementary Particles; Fourier transforms; Gravity; Helicity; Higher Spin Symmetry; Holography; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Space-Time Symmetries; Spacetime; String Theory; Symmetry; Wave functions; Classical Theories of Gravity; Space-Time Symmetries; Conformal and W Symmetry; Higher Spin Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2024)176

A bstract Celestial holography provides a reformulation of scattering amplitudes in four dimensional asymptotically flat spacetimes in terms of conformal correlators of operators on the two dimensional celestial sphere in a basis of boost eigenstates. A basis of massless particle states has been previously identified in terms of conformal primary wavefunctions labeled by a boost weight ∆ = 1+ iλ with λ ∈ ℝ. Here we show that a discrete orthogonal and complete basis exists for ∆ ∈ ℤ. This new basis consists of a tower of discrete memory and Goldstone observables, which are conjugate to each other and allow to reconstruct gravitational signals belonging to the Schwartz space. We show how generalized dressed states involving the whole tower of Goldstone operators can be constructed and evaluate the higher spin Goldstone 2-point functions. Finally, we recast the tower of higher spin charges providing a representation of the w 1+ ∞ loop algebra (in the same helicity sector) in terms of the new discrete basis.