  The random vector potential model describes massless fermions coupled to a
quenched random gauge field. We study its abelian and non-abelian versions. The
abelian version can be completely solved using bosonization. We analyse the
non-abelian model using its supersymmetric formulation and show, by a
perturbative renormalisation group computation, that it is asymptotically free
at large distances. We also show that all the quenched chiral current
correlation functions can be computed exactly, without using the replica trick
or the supersymmetric formulation, but using an exact expression for the
effective action for any sample of the random gauge field. These chiral
correlation functions are purely algebraic.
