#### Bulg. J. Phys. vol.35 no.s1 (2008), pp. 36- 42

#### Constructing Models of Vertex Algebras in Higher Dimensions

Bojko Bakalov

go back^{1}, Nikolay M. Nikolov^{2}^{1}*Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA*^{2}*Institute for Nuclear Research and Nuclear Energy, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria*Abstract.Vertex algebras in higher dimensions correspond to models of Quantum Field Theory (Wightman axioms) with Global Conformal Invariance. We review how such a vertex algebra can be generated from a collection of local fields, or from a vertex Lie algebra. The one-dimensional restriction of a vertex algebra in higher dimensions to a time-like line gives a chiral vertex algebra endowed with an action of the (higher-dimensional) conformal Lie algebra. We announce that from such data one can reconstruct the initial vertex algebra.