  For n\geq 2, there is a free field realization of the affine vertex
superalgebra A associated to psl(n|n) at critical level inside the
bc\beta\gamma system W of rank n^2. We show that the commutant C=Com(A,W) is
purely bosonic and is freely generated by n+1 fields. We identify the Zhu
algebra of C with the ring of invariant differential operators on the space of
n\times n matrices under SL_n \times SL_n, and we classify the irreducible,
admissible C-modules with finite dimensional graded pieces. For n\leq 4, C is
isomorphic to the W_n^{(2)}-algebra at critical level, and we conjecture that
this holds for all n.
