  We explore here the issue of duality versus spectrum equivalence in abelian
vector theories in 2+1 dimensions. Specifically we examine a generalized
self-dual (GSD) model where a Maxwell term is added to the self-dual model. A
gauge embedding procedure applied to the GSD model leads to a
Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show that the
latter contains a ghost mode contrary to the original GSD model. On the other
hand, the same embedding procedure can be applied to $N_f$ fermions minimally
coupled to the self-dual model. The dual theory corresponds to $N_f$ fermions
with an extra Thirring term coupled to the gauge field via a Pauli-like term.
By integrating over the fermions at $N_f\to\infty$ in both matter coupled
theories we obtain effective quadratic theories for the corresponding vector
fields. On one hand, we have a nonlocal type of the GSD model. On the other
hand, we have a nonlocal form of the MCS theory. It turns out that both
theories have the same spectrum and are ghost free. By figuring out why we do
not have ghosts in this case we are able to suggest a new master action which
takes us from the local GSD to a nonlocal MCS model with the same spectrum of
the original GSD model and ghost free. Furthermore, there is a dual map between
both theories at classical level which survives quantum correlation functions
up to contact terms. The remarks made here may be relevant for other
applications of the master action approach.
