Bulg. J. Phys. vol.34 no.3 (2007), pp. 204-215

Higher Dimensional Vertex Algebras and Rational Conformal Field Theory Models

I. Todorov1,2
1Institute for Nuclear Research and Nuclear Energy, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria
2Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
Abstract. The notion of global conformal invariance>/i> (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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