Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models

抄録

It is shown that (r−1)-state restricted eight-vertex SOS model (8VSOS) by Andrews, Baxter and Forrester is equivalent to q-state Potts model with q=4·cos²(π⁄r) (r=4, 5, 6…) at criticality. The equivalence follows from the Temperley-Lieb algebra shared by the models which is nothing but C^*-algebra A_q,n defined by Jones in von Neumann algebra theory. This implies the correspondence of indices for subfactors of type II₁ factors and discrete series of Virasoro algebra which labels the universality classes of the 8VSOS models.