To understand strongly coupled systems such as
quark confinement in QCD or quantum Hall
transitions is one of the most fundamental
challenges in theoretical physics. The best
understood examples of strongly coupled systems
arise in two (or 1+1) dimensional physics. For
instance it has been known for a long time that
the massless Thirring model - a theory of
fermions with quartic interactions - can be
equivalently described by a free boson. In this
duality the coupling constant of the Thirring
model should be interpreted as the radius of a
circle on which the free boson is compactified.
In this talk I will present evidence for a
duality between certain supersphere sigma-models
and a special kind of Gross-Neveu models which
provides a non-abelian generalization of the
previous correspondence. I will also indicate the
physical relevance of these models in the context
of loop ensembles (short: polymers) and string theory.