Harmonic bilocal fields generated by globally conformal invariant scalar fields
arXiv:0704.1960 · doi:10.1007/s00220-007-0394-0
Abstract
The twist two contribution in the operator product expansion of phi_1(x_1) phi_2(x_2) for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space-time dimensions is a field V_1(x_1,x_2) which is harmonic in both variables. It is demonstrated that the Huygens bilocality of V_1 can be equivalently characterized by a "single-pole property" concerning the pole structure of the (rational) correlation functions involving the product phi_1(x_1) phi_2(x_2). This property is established for the dimension d=2 of phi_1, phi_2. As an application we prove that any system of GCI scalar fields of conformal dimension 2 (in four space-time dimensions) can be presented as a (possibly infinite) superposition of products of free massless fields.
29 pages. v2: corrected an argument, v4: final version as to be published in CMP
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Cited by in corpus (11)
- D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
- Constraining conformal field theory with higher spin symmetry in four dimensions
- Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
- Quantum field theory in terms of consistency conditions I: General framework, and perturbation theory via Hochschild cohomology
- Conformal field theories with infinitely many conservation laws
- Infinite dimensional Lie algebras in 4D conformal quantum field theory
- Conformal quantum field theory in various dimensions
- New methods in conformal partial wave analysis
- Minimal representations and reductive dual pairs in conformal field theory
- Constructive use of holographic projections
- Studying Quantum Field Theory