MG14 - Talk detail

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The study of conformal field theory (CFT) in two space-time dimensions has found applications to different areas of physics and mathematics such as string theory, critical phenomena, infinite dimensional Lie algebras, number theory, finite simple groups, 3-manifold invariants, the theory of subfactors and noncommutative geometry. Chiral CFTs, i.e. CFTs on the circle, are the building blocks of CFT. We have two different mathematical formulations of chiral CFT: vertex operator algebras (VOAs) and conformal nets. The first is manly algebraic while the second, being the algebraic quantum field theory version of chiral CFT, is based on the theory of operator algebras on Hilbert spaces (C*-algebras and von Neumann algebras) and hence it is mainly (functional) analytic. In this talk I will explain some general results that allow to connect directly these two formulations of CFT. I will define a class of unitary simple VOAs called strongly local and explain how one can construct a conformal net from every strongly local VOA. I will explain various properties of this construction and give examples of strongly local VOAs. (Based on a joint work with Y. Kawahigashi, R. Longo and M. Weiner)

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