# From vertex operator superalgebras to graded-local conformal nets and back

April 27, 2023

We generalize the Carpi-Kawahigashi-Longo-Weiner correspondence between
vertex operator algebras and conformal nets to the case of vertex operator
superalgebras and graded-local conformal nets by introducing the notion of
strongly graded-local vertex operator superalgebra. Then we apply our machinery
to a number of well-known examples including superconformal field theory
models. We also prove that all lattice VOSAs are strongly graded-local.
Furthermore, we prove strong graded-locality of the super-Moonshine VOSA, whose
group of automorphisms preserving the superconformal structure is isomorphic to
Conway's largest sporadic simple group, and of the shorter Moonshine VOSA,
whose automorphisms group is isomorphic to the direct product of the baby
Monster with a cyclic group of order two.

Keywords:

*none*