$sl(2,\mathds{C})\times D$ symmetry and conformal primary basis for massless fields

Abstract

Alternative to the embedding formalism, we provide a group theoretic approach to the conformal primary basis for the massless field with arbitrary helicity. To this end, we first point out that $sl(2,\mathds{C})$ isometry gets enhanced to $sl(2,\mathds{C})\times D$ symmetry for the solution space of the massless field with arbitrary helicity. Then associated with $sl(2,\mathds{C})\times D$ symmetry, we introduce the novel quadratic Casimirs and relevant tensor/spinor fields to derive 2 explicit constraints on the bulk dilatation and $sl(2,\mathds{C})$ Casimirs. With this, we further argue that the candidate conformal primary basis can be constructed out of the infinite tower of the descendants of the left and right highest (lowest) conformal primary wavefunction of $sl(2,\mathds{C})$ Lie algebra, and the corresponding celestial conformal weights are determined by the bulk scaling dimension through solving out the exact on-shell conformal primary wavefunctions, where on top of the two kinds of familiar-looking on-shell conformal primary wavefunctions, we also obtain another set of independent on-shell conformal primary wavefunctions for the massless field with helicity $|s|\ge 1$. In passing, we also develop the relationship between the 4D Lorentz Lie algebra and 2D conformal Lie algebra from scratch, and present an explicit derivation for the two important properties associated with the conformal primary wavefunctions.

Typos corrected, references updated, version to appear in PRD, 16 pages, 4 tables

References in corpus (17)

• AdS3 Black Holes and a Stringy Exclusion Principle
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• Hidden Conformal Symmetry of the Kerr Black Hole
• A holographic reduction of Minkowski space-time
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Conformally Soft Photons and Gravitons
• Symmetries of Celestial Amplitudes
• Primary Fields in Celestial CFT
• Quasi-Normal Modes in Topologically Massive Gravity
• Conformal Primary Basis for Dirac Spinors
• Relativistic partial waves for celestial amplitudes
• Massive Spinning Bosons on the Celestial Sphere
• Implications of Superrotations
• $SL(2,R)$ symmetry and quasi-normal modes in the BTZ black hole
• $SL(2,R)\times U(1)$ symmetry and quasinormal modes in the self-dual warped AdS black hole