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# Advances in Theoretical and Mathematical Physics

## Volume 15 (2011)

### Number 5

### Symmetries of massless vertex operators in $AdS_5\times S^5$

Pages: 1319 – 1372

DOI: http://dx.doi.org/10.4310/ATMP.2011.v15.n5.a3

#### Author

#### Abstract

The worldsheet sigma-model of the superstring in $AdS_5\times S^5$ has aone-parameter family of flat connections parametrized by the spectralparameter. The corresponding Wilson line is not BRST invariant for an opencontour, because the BRST transformation leads to boundary terms. Theseboundary terms define a cohomological complex associated to the endpoint of thecontour. We study the cohomology of this complex for Wilson lines in someinfinite-dimensional representations. We find that for these representationsthe cohomology is nontrivial at the ghost number 2. This implies that it ispossible to define a BRST invariant open Wilson line.The central point in the construction is the existence of masslessvertex operators transforming exactly covariantly under the action of the global symmetrygroup. In flat space massless vertices transform covariantly only up to addingBRST exact terms. But in AdS we show that it is possible to define verticesso that they transform exactly covariantly.