Symmetries of massless vertex operators in $AdS_5 × S^5$

Abstract

The worldsheet sigma-model of the superstring in $AdS_5 × S^5$ 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.