$Ad{S}_5\times S^5$ supergravity vertex operators

Abstract

In any type II superstring background, the supergravity vertex operators in the pure spinor formalism are described by a gauge superfield. In this paper, we obtain for the first time an explicit expression for this superfield in an $Ad{S}_5\times S^5$ background. Previously, the vertex operators were only known close to the boundary of $Ad{S}_5$ or in the minus eight picture. Our strategy for the computation was to apply eight picture raising operators in the minus eight picture vertices. In the process, a huge number of terms are generated and we have developed numerical techniques to perform intermediary simplifications. Alternatively, the same numerical techniques can be used to compute the vertices directly in the zero picture by constructing a basis of invariants and fitting for the coefficients. One motivation for constructing the vertex operators is the computation of $Ad{S}_5\times S^5$ string amplitudes.

arXiv commentReferences added. Minor improvements

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Cited by in corpus (4)

• The AdS Virasoro-Shapiro Amplitude
• AdS Virasoro-Shapiro from single-valued periods
• Pure spinor formulation of the superstring and its applications
• Supersymmetric String Configurations in Ad${\mathbb{S}}_5\times {\mathbb{S}}^5$