Deformations of AdS and exact sequences

TL;DR

This paper explores cohomological deformations of AdS spaces within superconformal algebra, using pure spinor formalism to address obstacles in computing correlation functions in supergravity.

Contribution

It introduces a framework for analyzing cohomologies and deformations of AdS spaces, addressing non-covariance issues in BRST cohomology computations.

Findings

Examples of superconformal algebra cohomologies relevant to AdS supergravity.

Framework for describing cohomological obstacles using pure spinor formalism.

Conjectures about the structure of these obstacles.

Abstract

We give examples of cohomologies of the superconformal algebra, relevant to computations in the AdS supergravity. Our main examples are deformations of $AdS_5\times S^5$ 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.