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.
Publié le : 2003-08-25
Classification:
Mathematical Physics,
High Energy Physics - Theory,
Mathematics - Operator Algebras,
81T40,
81T05,
81R15,
46L37,
46L60
@article{0308029,
author = {Kawahigashi, Yasuyuki},
title = {Classification of operator algebraic conformal field theories in
dimensions one and two},
journal = {arXiv},
volume = {2003},
number = {0},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/0308029}
}
Kawahigashi, Yasuyuki. Classification of operator algebraic conformal field theories in
dimensions one and two. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0308029/