  The goal of this paper is to study the BMN correspondence in the fermionic
sector. On the field theory side, we compute matrix elements of the dilatation
operator in N=4 Super Yang-Mills for BMN operators containing two fermion
impurities. Our calculations are performed up to and including O(lambda') in
the 't Hooft coupling and O(g_2) in the Yang-Mills genus counting parameter. On
the string theory side, we compute the corresponding matrix elements of the
interacting string Hamiltonian in string field theory, using the three-string
interaction vertex constructed by Spradlin and Volovich (and subsequently
elaborated by Pankiewicz and Stefanski). In string theory we use the natural
string basis, and in field theory the basis which is isomorphic to it. We find
that the matrix elements computed in field theory and the corresponding string
amplitudes derived from the three-string vertex are, in all cases, in perfect
agreement.
