Conformal Primary Basis for Dirac Spinors

Abstract

We study solutions to the Dirac equation in Minkowski space ${\mathbb{R}}^{1,d+1}$ that transform as $d$-dimensional conformal primary spinors under the Lorentz group $SO(1,d+1)$. Such solutions are parameterized by a point in ${\mathbb{R}}^d$ and a conformal dimension $\Delta$. The set of wavefunctions that belong to the principal continuous series, $\Delta =\frac{d}{2}+i\nu$, with $\nu \ge 0$ and $\nu \in \mathbb{R}$ in the massive and massless cases, respectively, form a complete basis of delta-function normalizable solutions of the Dirac equation. In the massless case, the conformal primary wavefunctions are related to the wavefunctions in momentum space by a Mellin transform.

21 pages, v2: added references, v3: added calculation of the explicit form of the wave function

References in corpus (22)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Spinning Conformal Correlators
• Projectors, Shadows, and Conformal Blocks
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• Spinning Conformal Blocks
• A holographic reduction of Minkowski space-time
• Gluon Amplitudes as 2d Conformal Correlators
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Conformally Soft Photons and Gravitons
• Bootstrapping 3D Fermions
• Extended Super BMS Algebra of Celestial CFT
• Uplifting AdS3/CFT2 to Flat Space Holography
• Primary Fields in Celestial CFT
• Fermion-Scalar Conformal Blocks
• Relativistic partial waves for celestial amplitudes
• Massive Spinning Bosons on the Celestial Sphere
• New Methods for Conformal Correlation Functions
• On conformal correlators and blocks with spinors in general dimensions
• Poincaré Constraints on Celestial Amplitudes

Cited by in corpus (21)

• Lectures on Celestial Amplitudes
• Celestial Amplitudes from UV to IR
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Shifting Spin on the Celestial Sphere
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Lectures on Celestial Holography
• Loops on the Celestial Sphere
• State-Operator Correspondence in Celestial Conformal Field Theory
• Massive Celestial Fermions
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Conformally Soft Fermions
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Shadow Celestial Amplitude
• Celestial Supersymmetry
• Symmetries in Celestial CFT${}_d$
• Zwanziger's pairwise little group on the celestial sphere
• $p$-Forms on the Celestial Sphere
• Multiparticle Contributions to the Celestial OPE
• Celestial Holography
• $sl(2,\mathds{C})\times D$ symmetry and conformal primary basis for massless fields