Helicity basis for three-dimensional conformal field theory

Abstract

Three-point correlators of spinning operators admit multiple tensor structures compatible with conformal symmetry. For conserved currents in three dimensions, we point out that helicity commutes with conformal transformations and we use this to construct three-point structures which diagonalize helicity. In this helicity basis, OPE data is found to be diagonal for mean-field correlators of conserved currents and stress tensor. Furthermore, we use Lorentzian inversion formula to obtain anomalous dimensions for conserved currents at bulk tree-level order in holographic theories, which we compare with corresponding flat-space gluon scattering amplitudes.

arXiv comment37+23 pages, 5 figures. Typos fixed, published version

References in corpus (71)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• The Analytic Bootstrap and AdS Superhorizon Locality
• Spinning Conformal Correlators
• On graviton non-Gaussianities during inflation
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• Projectors, Shadows, and Conformal Blocks
• Conformal Regge theory
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Spinning Conformal Blocks
• Implications of conformal invariance in momentum space
• Light-ray operators in conformal field theory
• Radial Coordinates for Conformal Blocks
• Large Spin Perturbation Theory
• Spinning AdS Propagators
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Unitarity and the Holographic S-Matrix
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• The S-matrix Bootstrap I: QFT in AdS
• A spacetime derivation of the Lorentzian OPE inversion formula
• Analyticity and the Holographic S-Matrix
• New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators
• Gravitational S-matrix from CFT dispersion relations
• Local bulk S-matrix elements and CFT singularities
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Weight Shifting Operators and Conformal Blocks
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Einstein gravity 3-point functions from conformal field theory
• TASI Lectures on the Conformal Bootstrap
• Universal anomalous dimensions at large spin and large twist
• Analytic bootstrap at large spin
• Harmonic Analysis and Mean Field Theory
• Bounds for OPE coefficients on the Regge trajectory
• The 3d Stress-Tensor Bootstrap
• Bootstrapping 3D Fermions with Global Symmetries
• Shocks, Superconvergence, and a Stringy Equivalence Principle
• Light-Front Bootstrap for Chern-Simons Matter Theories
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• On duality of color and kinematics in (A)dS momentum space
• Conformal correlators of mixed-symmetry tensors
• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• Color/Kinematics Duality in AdS${}_4$
• Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
• Landau diagrams in AdS and S-matrices from conformal correlators
• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• Radial expansion for spinning conformal blocks
• String scattering in flat space and a scaling limit of Yang-Mills correlators
• Flat space physics from AdS/CFT
• Momentum space approach to crossing symmetric CFT correlators
• Renormalization group coefficients and the S-matrix
• Unitarity Methods in AdS/CFT
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• Casimir recursion relations for general conformal blocks
• Large spin systematics in CFT
• New relation for AdS amplitudes
• Notes on flat-space limit of AdS/CFT
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Recursion relation for general 3d blocks
• From bulk loops to boundary large-N expansion
• Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories
• From Scattering Amplitudes to the Dilatation Generator in N=4 SYM
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$
• blocks_3d: Software for general 3d conformal blocks
• Closed-form expression for cross-channel conformal blocks near the lightcone
• Lightcone expansions of conformal blocks in closed form
• Factorized lightcone expansion of conformal blocks

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• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Hidden Relations of Central Charges and OPEs in Holographic CFT
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