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<p>We give examples of cohomologies of the superconformal algebra, relevant to computations in the AdS supergravity. Our main examples are deformations of <i>AdS</i><sub>5</sub> × <i>S</i><sup>5</sup> 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.</p>

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Deformations of AdS and exact sequences

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月5日

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  • Andrei Mikhailov

摘要

We give examples of cohomologies of the superconformal algebra, relevant to computations in the AdS supergravity. Our main examples are deformations of AdS5 × S5 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.