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 $2-\Delta$. The Dirac conformal primary wavefunctions are delta function normalizable with respect to the Dirac inner product provided they lie on the principal series with conformal dimension $\Delta =1+i\lambda$ for $\lambda \in \mathbb{R}$. It is shown that there are two choices of a complete basis: single spin $J=\frac{1}{2}$ or $J=-\frac{1}{2}$ and $\lambda \in \mathbb{R}$ or multiple spin $J=\pm \frac{1}{2}$ and $\lambda \in {\mathbb{R}}_{+\cup 0}$. 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 Poincare 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-$\frac{1}{2}$.

arXiv comment12 pages + 4 pages of appendices; v2 minor typos fixed and small clarifications added

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• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• State-Operator Correspondence in Celestial Conformal Field Theory
• Celestial double copy from the worldsheet
• Asymptotic dynamics on the worldline for spinning particles
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations
• The structure of IR divergences in celestial gluon amplitudes
• Conformally Soft Fermions
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Shadow Celestial Amplitude
• Celestial Supersymmetry
• Symmetries in Celestial CFT${}_d$
• Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity
• $p$-Forms on the Celestial Sphere
• Zwanziger's pairwise little group on the celestial sphere
• Multiparticle Contributions to the Celestial OPE
• On the geometric approach to the boundary problem in supergravity