  It has been argued in previous works by the authors that nodal excitations in
(2+1)-dimensional doped antiferromagnets might exhibit, in the spin-charge
separation framework and at specific regions of the parameter space, a
supersymmetry between spinons and holons. This supersymmetry has been elevated
to a N=2 extended supersymmetry of composite operators of spinon and holons,
corresponding to the effective "hadronic" degrees of freedom. In this work we
elaborate further on this idea by describing in some detail the dynamics of a
specific composite model corresponding to an Abelian Higgs model (SQED). The
abelian nature of the gauge group seems to be necessitated both by the
composite structure used, but also by electric charge considerations for the
various composites. We demonstrate the passage from a pseudogap to an
unconventional superconducting phase, which notably is an exact
non-perturbative analytic result, due to the underlying N=2 supersymmetric
Abelian gauge theory. We believe that these considerations may provide a first
step towards a non-perturbative understanding of the phase diagrams of
strongly-correlated electron systems.
