Higher spin 3-point functions in 3d CFT using spinor-helicity variables

Abstract

In this paper we use the spinor-helicity formalism to calculate 3-point functions involving scalar operators and spin-$s$ conserved currents in general 3d CFTs. In spinor-helicity variables we notice that the parity-even and the parity-odd parts of a correlator are related. Upon converting spinor-helicity answers to momentum space, we show that correlators involving spin-$s$ currents can be expressed in terms of some simple conformally invariant conserved structures. This in particular allows us to understand and separate out contact terms systematically, especially for the parity-odd case. We also reproduce some of the correlators using weight-shifting operators.

arXiv commentv1: 59 pages, v2: A few typos corrected, v3 : Appendix G added

References in corpus (52)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning Conformal Correlators
• On graviton non-Gaussianities during inflation
• Implications of conformal invariance in momentum space
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Bootstrapping Inflationary Correlators in Mellin Space
• Analyticity and the Holographic S-Matrix
• New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• Local bulk S-matrix elements and CFT singularities
• A Mellin Space Approach to Cosmological Correlators
• CMB from CFT
• Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
• Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
• Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation
• Double copy structure of CFT correlators
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• Light-Front Bootstrap for Chern-Simons Matter Theories
• Conformal $n$-point functions in momentum space
• On duality of color and kinematics in (A)dS momentum space
• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• Color/Kinematics Duality in AdS${}_4$
• Landau diagrams in AdS and S-matrices from conformal correlators
• Momentum space approach to crossing symmetric CFT correlators
• Lorentzian CFT 3-point functions in momentum space
• The flat space S-matrix from the AdS/CFT correspondence?
• Double copy structure and the flat space limit of conformal correlators in even dimensions
• Multipoint correlators of conformal field theories: implications for quantum critical transport
• Momentum-space conformal blocks on the light cone
• Conformal correlators as simplex integrals in momentum space
• An étude of momentum space scalar amplitudes in AdS
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• New relation for AdS amplitudes
• Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension
• Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative $TJJ$ Vertex
• Double copy structure of parity-violating CFT correlators
• Towards the higher point holographic momentum space amplitudes II: Gravitons
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• On Some Hypergeometric Solutions of the Conformal Ward Identities of Scalar 4-point Functions in Momentum Space
• On spinning loop amplitudes in Anti-de Sitter space
• Momentum space spinning correlators and higher spin equations in three dimensions
• Conserved current correlators of conformal field theories in 2+1 dimensions
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Renormalization, Conformal Ward Identities and the Origin of a Conformal Anomaly Pole
• Convergent Momentum-Space OPE and Bootstrap Equations in Conformal Field Theory
• A Scattering Amplitude in Conformal Field Theory
• Four-Point Functions in Momentum Space: Conformal Ward Identities in the Scalar/Tensor case
• Conformal partial waves in momentum space
• The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field
• Conformal Ward Identities and the Coupling of QED and QCD to Gravity

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• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• A handbook of holographic 4-point functions
• On Graviton non-Gaussianities in the Effective Field Theory of Inflation
• Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound
• Momentum space CFT correlators of non-conserved spinning operators
• Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
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• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
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• The Hilbert Space of large $N$ Chern-Simons matter theories
• Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins
• On correlation functions as higher-spin invariants
• Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory
• Spinors and conformal correlators
• $n$-point functions in Conformal Quantum Mechanics: A Momentum Space Odyssey
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Three-point functions of fermionic higher-spin currents in 4D conformal field theory