Bulg. J. Phys. vol.33 no.s1 (2006), pp. 69-80


Higher Dimensional Vertex Algebras and Rational Conformal Field Theory Models

I. Todorov
Institute for Nuclear Research and Nuclear Energy, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria
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 4-point level for D=4, and a study of modular properties of thermal expectation values of the conformal energy operator.

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