  We study deformed WZW models on supergroups with vanishing Killing form. The
deformation is generated by the isotropic current-current perturbation which is
exactly marginal under these assumptions. It breaks half of the global
isometries of the original supergroup. The current corresponding to the
remaining symmetry is conserved but its components are neither holomorphic nor
anti-holomorphic. We obtain the exact two- and three-point functions of this
current and a four-point function in the first two leading orders of a 1/k
expansion but to all orders in the deformation parameter. We further study the
operator product algebra of the currents, the equal time commutators and the
quantum equations of motion. The form of the equations of motion suggests the
existence of non-local charges which generate a Yangian. Possible applications
to string theory on Anti-de Sitter spaces and to condensed matter problems are
briefly discussed.
