On the construction of integrated vertex in the pure spinor formalism in curved background

Abstract

We have previously described a way of describing the relation between unintegrated and integrated vertex operators in AdS(5) x S-5 which uses the interpretation of the BRST cohomology as a Lie algebra cohomology and integrability properties of the AdS background. Here we clarify some details of that description, and develop a similar approach for an arbitrary curved background with nondegenerate RR bispinor. For an arbitrary curved background, the sigma-model is not integrable. However, we argue that a similar construction still works using an infinite-dimensional Lie algebroid. (C) 2016 Published by Elsevier B.V.