Massive celestial fermions

Abstract

In an effort to further the study of amplitudes in the celestial CFT (CCFT), we construct conformal primary wavefunctions for massive fermions. Upon explicitly calculating the wavefunctions for Dirac fermions, we deduce the corresponding transformation of momentum space amplitudes to celestial amplitudes. The shadow wavefunctions are shown to have opposite spin and conformal dimension 2 − ∆. The Dirac conformal primary wave- functions are delta function normalizable with respect to the Dirac inner product provided they lie on the principal series with conformal dimension ∆ = 1 + iλ for λ ∈ ℝ. It is shown that there are two choices of a complete basis: single spin $$ J=\frac{1}{2} $$ J = 1 2 or $$ J=-\frac{1}{2} $$ J = − 1 2 and λ ∈ ℝ or multiple spin $$ J=\pm \frac{1}{2} $$ J = ± 1 2 and λ ∈ ℝ+∪0. The massless limit of the Dirac conformal primary wavefunctions is shown to agree with previous literature. The momentum generators on the celestial sphere are derived and, along with the Lorentz generators, form a representation of the Poincaré algebra. Finally, we show that the massive spin-1 conformal primary wavefunctions can be constructed from the Dirac conformal primary wavefunctions using the standard Clebsch-Gordan coefficients. We use this procedure to write the massive spin-$$ \frac{3}{2} $$ 3 2 , Rarita-Schwinger, conformal primary wavefunctions. This provides a prescription for constructing all massive fermionic and bosonic conformal primary wavefunctions starting from spin-$$ \frac{1}{2} $$ 1 2 .

State-operator correspondence in celestial conformal field theory

“…Similar inner products can be constructed from symplectic structures [17] for arbitrary integer spin J. The treatment of half-integer spin J requires an inner product like the Dirac inner product considered in [18][19][20].…”

Celestial double copy from the worldsheet

“…These wavefunctions transform as conformal primaries up to gauge transformations [3]. Wavefunctions for massive particles have also been worked out [42,43] but we won't have anything to say about massive particles. Amplitudes are in principle computed using (2.1) and (2.2) as external wavefunctions, but it is more convenient to simply Mellin transform the usual amplitudes computed with plane waves.…”

Asymptotic dynamics on the worldline for spinning particles

“…For both gauge theories and gravity, the use of worldline techniques in the study of asymptotic dynamics can be also analyzed in the light of the revived interest in the Faddeev-Kulish coherent states [77][78][79][80][81][82][83][84][85][86][87], where the GWL offers a natural way to extend the analysis at subleading power in the soft expansion. In particular, the recently proposed prescription to define an infrared-finite S-matrix [89] provides a modern derivation of the asymptotic Hamiltonian in terms of Wilson lines and effective field theory techniques.…”

“…However, the GWL have a much broader scope, which offers other motivations for the present study. One arises from a revived interest in asymptotic states à la Faddeev-Kulish [74][75][76][77][78][79][80][81][82][83][84][85][86][87]. Most of these methods revolve around the existence of an asymptotic Hamiltonian governing the evolution of the asymptotic states.…”