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Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
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RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.35 no.s1 (2008), pp. 36- 42
Constructing Models of Vertex Algebras in Higher Dimensions
Bojko Bakalov1, Nikolay M. Nikolov2
1Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA
2Institute for Nuclear Research and Nuclear Energy, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria
go back1Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA
2Institute 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.