Massive celestial fermions

Journal Article · Thu Dec 10 00:00:00 EST 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep12(2020)074· OSTI ID:1851022

Narayanan, Sruthi A. ^[1]

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1. Harvard Univ., Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States)

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 - Δ. 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 Δ = 1 + iλ for λ ∈ $$\mathbb{R}$$. It is shown that there are two choices of a complete basis: single spin J=$$\frac{1}{2}$$ or J=-$$\frac{1}{2}$$ and λ ∈ $$\mathbb{R}$$ or multiple spin J=±$$\frac{1}{2}$$ and λ $$\mathbb{R}$$_+∪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-$$\frac{3}{2}$$, Rarita-Schwinger, conformal primary wavefunctions. This provides a prescription for constructing all massive fermionic and bosonic conformal primary wavefunctions starting from spin-$$\frac{1}{2}$$.

• Research Organization: Harvard Univ., Cambridge, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0007870
• OSTI ID: 1851022
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2020; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
conformal and W symmetry
conformal field theory
scattering amplitudes