Conformal invariance and rationality in an even dimensional quantum field theory

TL;DR

This paper explores how conformal invariance in higher-dimensional quantum field theories leads to strong locality and rational correlation functions, extending vertex algebra concepts and examining finite temperature effects.

Contribution

It extends the concept of vertex algebra to higher dimensions through conformal invariance and investigates a scalar field model with potential gauge theory applications.

Findings

Correlation functions are rational due to conformal invariance.

Finite temperature expectation values are elliptic functions.

A model of a scalar field with conformal symmetry is constructed.

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.