On the uniqueness of diffeomorphism symmetry in Conformal Field Theory
arXiv:math/0407190 · doi:10.1007/s00220-005-1335-4
Abstract
A Moebius covariant net of von Neumann algebras on S^1 is diffeomorphism covariant if its Moebius symmetry extends to diffeomorphism symmetry. We prove that in case the net is either a Virasoro net or any at least 4-regular net such an extension is unique: the local algebras together with the Moebius symmetry (equivalently: the local algebras together with the vacuum vector) completely determine it. We draw the two following conclusions for such theories. (1) The value of the central charge c is an invariant and hence the Virasoro nets for different values of c are not isomorphic as Moebius covariant nets. (2) A vacuum preserving internal symmetry always commutes with the diffeomorphism symmetries. We further use our result to give a large class of new examples of nets (even strongly additive ones), which are not diffeomorphism covariant; i.e. which do not admit an extension of the symmetry to Diff^+(S^1).
arXiv comment25 pages, LaTeX
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