  We propose a correspondence between vertex operator superalgebras and
families of sigma models in which the two structures are related by symmetry
properties and a certain reflection procedure. The existence of such a
correspondence is motivated by previous work on N=(4,4) supersymmetric
non-linear sigma models on K3 surfaces and on a vertex operator superalgebra
with Conway group symmetry. Here we present an example of the correspondence
for N=(4,4) supersymmetric non-linear sigma models on four-tori, and compare it
to the K3 case.
