We study two-dimensional conformal field theories generated from a
``symplectic fermion'' - a free two-component fermion field of spin one - and
construct the maximal local supersymmetric conformal field theory generated
from it. This theory has central charge c=-2 and provides the simplest example
of a theory with logarithmic operators.
Twisted states with respect to the global SL(2,C)-symmetry of the symplectic
fermions are introduced and we describe in detail how one obtains a consistent
set of twisted amplitudes. We study orbifold models with respect to finite
subgroups of SL(2,C) and obtain their modular invariant partition functions. In
the case of the cyclic orbifolds explicit expressions are given for all two-,
three- and four-point functions of the fundamental fields. The C_2-orbifold is
shown to be isomorphic to the bosonic local logarithmic conformal field theory
of the triplet algebra encountered previously. We discuss the relation of the
C_4-orbifold to critical dense polymers.Comment: LaTeX2e, 30 page
