N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

70 Conclusions and Outlook
likely to exist only in harmonic superspace, which admits unconstrained prepotentials
for N = 2 vector multiplets that could serve as the necessary auxiliary superfields.
In fact, the superfield constraints we have found in this thesis can readily be converted
into constraints on a corresponding harmonic superfield, cf. [2]. However, presumably
the 2-forms have to be embedded in other multiplets than the ones of the vector-tensor
variety, since the latter always introduce in addition as many vectors as there are
tensors, which is likely to prevent a formulation of pure Freedman-Townsend models.
The only other multiplet known to include a 2-form gauge field (apart from the yet
to be constructed double-tensor multiplet which, as the name suggests, would hardly
be an alternative) is the so-called tensor multiplet [7] we have encountered briefly in
section 1.2.
Finally, we note that also the purely bosonic Henneaux-Knaepen models deserve further
study concerning a possible extension of the Chern-Simons couplings. As has been
shown in the last chapter, the gauge field part of the nonlinear vector-tensor multiplet
with local central charge hints at a generalization that exceeds the one included already
in [28] and in our exposition of the models in section 3.5.