Pole structure and biharmonic fields in conformal QFT in four dimensions

Abstract

Imposing Huygens' Principle in a 4D Wightman QFT puts strong constraints on its algebraic and analytic structure. These are best understood in terms of ``biharmonic fields'', whose properties reflect the presence of infinitely many conserved tensor currents. In particular, a universal third-order partial differential equation is derived for the most singular parts of connected scalar correlation functions. This PDE gives rise to novel restrictions on the pole structure of higher correlation functions. An example of a six-point function is presented that cannot arise from free fields. This example is exploited to study the locality properties of biharmonic fields.

12 pages

References in corpus (4)

• Four Dimensional CFT Models with Rational Correlation Functions
• Partial wave expansion and Wightman positivity in conformal field theory
• Jacobi Identity for Vertex Algebras in Higher Dimensions
• Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields

Cited by in corpus (6)

• Constraining conformal field theory with higher spin symmetry in four dimensions
• Harmonic bilocal fields generated by globally conformal invariant scalar fields
• Conformal field theories with infinitely many conservation laws
• Conformal quantum field theory in various dimensions
• Minimal representations and reductive dual pairs in conformal field theory
• Studying Quantum Field Theory