Rationality of conformally invariant local correlation functions on compactified Minkowski space

Abstract

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification of Minkowski space and yields a strong form of locality valid for all non-isotropic intervals if assumed true for space-like separations.

20 pages, LATEX, amsfonts, latexsym

References in corpus (1)

• Large N Field Theories, String Theory and Gravity

Cited by in corpus (30)

• Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
• Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory
• Constraining conformal field theory with higher spin symmetry in four dimensions
• Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory
• Four Dimensional CFT Models with Rational Correlation Functions
• Globally conformal invariant gauge field theory with rational correlation functions
• Partial wave expansion and Wightman positivity in conformal field theory
• Harmonic bilocal fields generated by globally conformal invariant scalar fields
• Jacobi Identity for Vertex Algebras in Higher Dimensions
• Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
• On Conformal Infinity and Compactifications of the Minkowski Space
• Conformal field theories with infinitely many conservation laws
• Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT
• Lectures on Elliptic Functions and Modular Forms in Conformal Field Theory
• Infinite dimensional Lie algebras in 4D conformal quantum field theory
• Conformal invariance and rationality in an even dimensional quantum field theory
• Conformal quantum field theory in various dimensions
• Pole structure and biharmonic fields in conformal QFT in four dimensions
• Lectures on Algebraic Quantum Field Theory and Operator Algebras
• Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces
• New methods in conformal partial wave analysis
• Minimal representations and reductive dual pairs in conformal field theory
• Global Conformal Invariance and Bilocal Fields with Rational Correlation Functions
• Complex velocity transformations and the Bisognano--Wichmann theorem for quantum fields acting on Krein spaces
• Superconformal vertex algebras in four dimensions
• Massless Wigner particles in conformal field theory are free
• On invariants and scalar chiral correlation functions in N=1 superconformal field theories
• Studying Quantum Field Theory
• Semi-Differential Operators and the Algebra of Operator Product Expansion of Quantum Fields
• Reconstruction of vertex algebras in even higher dimensions