Abstract
We construct higher spin quasinormal modes algebraically in D-dimensional de Sitter spacetime using the ambient space formalism. The quasinormal modes fall into two nonunitary lowest-weight representations of mathfrak{so} (1, D). From a local QFT point of view, the lowest-weight quasinormal modes of massless higher spin fields are produced by gauge-invariant boundary conserved currents and boundary higher-spin Weyl tensors inserted at the southern pole of the past boundary. We also show that the quasinormal spectrum of a massless/massive spin-s field is precisely encoded in the Harish-Chandra character corresponding to the unitary massless/massive spin-s SO(1, D) representation.
Highlights
One standard method of finding quasinormal modes in a generic background with a horizon is solving the equation of motion for a perturbation, in most cases numerically, and imposing in-falling boundary condition at the horizon [2,3,4,5]
In this paper we will focus on generalizing the algebraic approach to construct quasinormal modes of higher spin fields, which are formulated in the ambient space
The least damped quasinormal modes of photons and gravitons in dSd+1 have quasinormal frequency iω = d − 1 and iω = d respectively. This result is inconsistent with [7], where the author finds that the lowest quasinormal frequency of photons and gravitons is iω = 2.5 The mismatch indicates that the α(s)-tower itself is not the end of the story and we have to modify our algebraic construction in the massless case to incorporate those missed quasinormal modes
Summary
To gain some intuitions about the ambient space description in field theory, let’s consider a free scalar field φ(y), defined in the local coordinates yμ, of mass m2 = ∆(d − ∆) and satisfying equation of motion: ∇2φ = m2φ with ∇2 being the scalar Laplacian. The obvious technical advantage of this ambient space description is replacing the cumbersome covariant derivative ∇μ by the simple ordinary derivative ∂XA. Such a simplification is more crucial when we deal with higher spin fields. We present an adapted version of the ambient space description in dS
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