Vertex (Lie) algebras in higher dimensions

Details Vertex (Lie) algebras in higher dimensions Vertex (Lie) algebras in higher dimensions

2006-08-23

arxiv.org/abs/math-ph/0608054v1

Physics

Mathematical Physics

Hermann Weyl prize lecture presented at the 26th International Colloquium on Group Theoretical Methods in Physics, New York, J

Scientific paper

Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE, or, equivalently, the commutators of chiral fields. We discuss generalizations of vertex algebras and vertex Lie algebras, which are relevant for higher-dimensional quantum field theory.

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