  This paper carries on the investigation of the non-unitary su(2)_{-1/2} WZW
model. An essential tool in our first work on this topic was a free-field
representation, based on a c=-2 \eta\xi ghost system, and a Lorentzian boson.
It turns out that there are several ``versions'' of the \eta\xi system,
allowing different su(2)_{-1/2} theories. This is explored here in details. In
more technical terms, we consider extensions (in the c=-2 language) from the
small to the large algebra representation and, in a further step, to the full
symplectic fermion theory. In each case, the results are expressed in terms of
su(2)_{-1/2} representations. At the first new layer (large algebra),
continuous representations appear which are interpreted in terms of relaxed
modules. At the second step (symplectic formulation), we recover a logarithmic
theory with its characteristic signature, the occurrence of indecomposable
representations. To determine whether any of these three versions of the
su(2)_{-1/2} WZW is well-defined, one conventionally requires the construction
of a modular invariant. This issue, however, is plagued with various
difficulties, as we discuss.
