  We derive the current algebra of supersymmetric principal chiral models with
a Wess-Zumino term. At the critical point one obtains two commuting super
Kac-Moody algebra as expected, but in general there are intertwining fields
connecting both right and left sectors, analogously to the bosonic case.
Moreover, in the present supersymmetric extension we have a quadratic algebra,
rather than an affine Lie algebra, due to the mixing between bosonic and
fermionic fields since the purely fermionic sector displays a Lie algebra as
well.
