On Z₂-twisted representation of vertex operator superalgebras and the Ising model SVOA

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We investigate a general theory of the Z₂-twisted representations of vertex operator superalgebras. Certain one-to-one correspondence theorems are established. We also give an explicit realization of the Ising model SVOA and its Z₂-twisted modules. As an application, we obtain the Gerald Hoehn's Babymonster SVOA VB and its Z₂-twisted module VBtw from the moonshine VOA V by cutting off the Ising models. It is also shown in this paper that Aut (VB) is finite.