Conformal invariance and rationality in an even dimensional quantum field theory

Abstract

Invariance under finite conformal transformations in Minkowski space and the Wightman axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of vertex algebra to higher dimensions. Gibbs (finite temperature) expectation values appear as elliptic functions in the conformal time. We survey and further pursue our program of constructing a globally conformal invariant model of a hermitean scalar field L of scale dimension four in Minkowski space-time which can be interpreted as the Lagrangian density of a gauge field theory.

33 pages, misprints corrected, references updated

References in corpus (5)

• Conformal Partial Waves and the Operator Product Expansion
• 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
• Elliptic functions and temperature inversion symmetry on spheres

Cited by in corpus (5)

• Partial wave expansion and Wightman positivity in conformal field theory
• Two-dimensional models as testing ground for principles and concepts of local quantum physics
• Lectures on Elliptic Functions and Modular Forms in Conformal Field Theory
• Massless Wigner particles in conformal field theory are free
• Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas