Vertex algebras and conformal field theory models in four dimensions

Abstract

The notion of global conformal invariance (GCI) in Minkowski space allows to prove rationality of correlation functions and to extend the concept of vertex algebra to any number D of space-time dimensions. The case of even D, which includes a conformal stress-energy tensor with a rational 3-point function, is of particular interest. Recent progress, reviewed in the talk, includes a full account of Wightman positivity at the 4point level for D=4, and a study of modular properties of thermal expectation values of the conformal energy operator.

Massless Wigner particles in conformal field theory are free

“…There are more claims that conformal fields with massless particles are free with different assumptions [38,39]. An advantage of our approach is to avoid any field-theoretic calculation.…”

Harmonic Bilocal Fields Generated by Globally Conformal Invariant Scalar Fields

“…The last two references are chiefly concerned with the case d = 4 (in D = 4 space-time dimensions) which appears to be of particular interest as corresponding to a (gauge invariant) Lagrangian density. The intermediate case d = 3 is briefly surveyed in[18].…”