Deformations of AdS and exact sequences

Abstract

We give examples of cohomologies of the superconformal algebra, relevant to computations in the AdS supergravity. Our main examples are deformations of $Ad{S}_5\times S^5$ transforming in finite-dimensional representations of the superconformal algebra at the linearized level. In the study of correlation functions, it is important to compute the resolution of BRST-exact products of vertex operators. The resolution is typically non-covariant, because of cohomological obstacles. Using the pure spinor formalism, we develop a framework to describe these obstacles, and formulate conjectures about their structure.

23 pp, LaTeX; v2: extended Introduction, added section on open questions; v3: corrections in Sections 9 and 11