  The worldsheet sigma-model of the superstring in AdS(5) x S(5) has a
one-parameter family of flat connections parametrized by the spectral
parameter. The corresponding Wilson line is not BRST invariant for an open
contour, because the BRST transformation leads to boundary terms. These
boundary terms define a cohomological complex associated to the endpoint of the
contour. We study the cohomology of this complex for Wilson lines in some
infinite-dimensional representations. We find that for these representations
the cohomology is nontrivial at the ghost number 2. This implies that it is
possible to define a BRST invariant open Wilson line. The central point in the
construction is the existence of massless vertex operators transforming exactly
covariantly under the action of the global symmetry group. In flat space
massless vertices transform covariantly only up to adding BRST exact terms. But
in AdS we show that it is possible to define vertices so that they transform
exactly covariantly.
