关于共形域论中同态对称性的唯一性
On the uniqueness of diffeomorphism symmetry in Conformal Field Theory
摘要：
S^1上von Neumann代数的Moebius协变网是同构协变的，如果它的Moebius对称扩展到同构对称。我们证明了当网是Virasoro网或任何至少4-正则网格时，这样的扩张是唯一的：局部代数与Moebius对称性（等价于：局部代数与真空向量）完全决定了它。(1)中心电荷c的值是不变量，因此不同c值的Virasoro网与Moebius协变网不是同构的。(2)保持真空的内部对称性总是与复同态对称性交换。我们进一步利用我们的结果给出了一大类新的网（甚至是强加性的网）的例子，它们不是同构协变的，也就是说，它们不允许对称性扩展到Diff^+（S^1）。
英文摘要：
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).
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