Classification of operator algebraic conformal field theories in dimensions one and two

Details Classification of operator algebraic conformal field theories in dimensions one and two Classification of operator algebraic conformal field theories in dimensions one and two

2003-08-25

arxiv.org/abs/math-ph/0308029v1

Physics

Mathematical Physics

For the proceedings of XIV International Congress on Mathematical Physics at Lisbon in 2003

Scientific paper

We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of a two-dimensional theory into two chiral theories. We give the first classification result of such chiral theories with representation theoretic invariants. That is, we use the central charge as the first invariant, and if it is less than 1, we obtain a complete classification. Our classification list contains a new net which does not seem to arise from the known constructions such as the coset or orbifold constructions. We also present a classification of full two-dimensional conformal theories. These are joint works with Roberto Longo.

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