From Schwinger to Wightman: all conformal 3-point functions in momentum space
arXiv:2109.15140
Abstract
All conformal correlation functions of 3 scalar primary operators are constructed in an axiomatic way, relying only on conformal symmetry and causality. The construction makes use of the R-product and its analyticity properties in Minkowski momentum space. The R-product is completely determined by a system of partial differential equations (the Ward identities for conformal transformations) and a boundary condition (permutation symmetry), up to an OPE coefficient. Wightman functions and time-ordered products are then derived from the R-product using operator identities, and the Schwinger function is recovered after a Wick rotation to Euclidean space. This construction does not rely on the Fourier transform of position-space correlation functions.
arXiv comment34 pages
References in corpus (16)
- Implications of Conformal Invariance in Field Theories for General Dimensions
- Projectors, Shadows, and Conformal Blocks
- Implications of conformal invariance in momentum space
- Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
- From dS to AdS and back
- The 3d Stress-Tensor Bootstrap
- Renormalised 3-point functions of stress tensors and conserved currents in CFT
- The Inflationary Wavefunction from Analyticity and Factorization
- Lorentzian CFT 3-point functions in momentum space
- Momentum-space conformal blocks on the light cone
- TTT in CFT: Trace Identities and the Conformal Anomaly Effective Action
- Momentum space conformal three-point functions of conserved currents and a general spinning operator
- Helicity basis for three-dimensional conformal field theory
- Conformal partial waves in momentum space
- Conformal Contact Terms and Semi-Local Terms
- Causality, Crossing and Analyticity in Conformal Field Theories