sl(2,C)×D symmetry and conformal primary basis for massless fields

Author:

Chen Yuan1,Li Mingfeng1,Shi Kai1,Zhang Hongbao11ORCID,Zhang Jingchao12

Affiliation:

1. Beijing Normal University

2. University of Michigan

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,C) isometry gets enhanced to sl(2,C)×D symmetry for the solution space of the massless field with D the bulk dilatation. Then, associated with sl(2,C)×D symmetry, we introduce the novel quadratic Casimirs and relevant tensor/spinor fields to derive two explicit constraints on the bulk dilatation and sl(2,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 wave function of sl(2,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 wave functions, where on top of the two kinds of familiar-looking on-shell conformal primary wave functions, we also obtain another set of independent on-shell conformal primary wave functions for the massless field with helicity |s|1. In passing, we also develop the relationship between the four-dimensional Lorentz Lie algebra and two-dimensional conformal Lie algebra from scratch, and present an explicit derivation for the two important properties associated with the conformal primary wave functions. Published by the American Physical Society 2024

Funder

National Key Research and Development Program of China

National Natural Science Foundation of China

Publisher

American Physical Society (APS)

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