Momentum space CFT correlators of non-conserved spinning operators

Abstract

We analyse the 3-point CFT correlators involving non-conserved spinning operators in momentum space. We derive a general expression for the conformal Ward identities defining the 3-point functions involving two generic spin $s$ non-conserved operators and a spin 1 conserved current. We give explicit expressions for the 3-point function when the two non-conserved operators have spins 1 and 2 and generic conformal dimensions. We also systematically analyse the divergences appearing in these 3-point functions when the conformal dimensions of the two non-conserved operators coincide.

arXiv comment33 pages + appendices

References in corpus (47)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Spinning Conformal Correlators
• On graviton non-Gaussianities during inflation
• Implications of conformal invariance in momentum space
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• Holography for Cosmology
• Conformal consistency relations for single-field inflation
• Bootstrapping Inflationary Correlators in Mellin Space
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• A Mellin Space Approach to Cosmological Correlators
• CMB from CFT
• Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
• Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter
• Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
• Holography for inflation using conformal perturbation theory
• Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
• 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
• Conformal $n$-point functions in momentum space
• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• Holographic predictions for cosmological 3-point functions
• Momentum space approach to crossing symmetric CFT correlators
• Lorentzian CFT 3-point functions in momentum space
• Double copy structure and the flat space limit of conformal correlators in even dimensions
• Evaluation of conformal integrals
• 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
• Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension
• 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
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Momentum space parity-odd CFT 3-point functions
• The General 3-Graviton Vertex ($TTT$) of Conformal Field Theories in Momentum Space in $d=4$
• On the power spectrum of inflationary cosmologies dual to a deformed CFT
• Momentum space spinning correlators and higher spin equations in three dimensions
• Constraining momentum space correlators using slightly broken higher spin symmetry
• A handbook of holographic 4-point functions
• Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound
• Four-Point Functions in Momentum Space: Conformal Ward Identities in the Scalar/Tensor case
• TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions
• Shift operators from the simplex representation in momentum-space CFT