$AdS_5 \times S^5$ supergravity vertex operators

TL;DR

This paper derives an explicit supergravity vertex operator in the $AdS_5 imes S^5$ background within the pure spinor formalism, enabling more precise string amplitude calculations in this important setting.

Contribution

It provides the first explicit expression for supergravity vertex operators in $AdS_5 imes S^5$, advancing the understanding of string interactions in this background.

Findings

Explicit supergravity vertex operator derived

Numerical techniques developed for intermediary simplifications

Potential for improved $AdS_5 imes S^5$ string amplitude computations

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 $AdS_5 \times S^5$ background. Previously, the vertex operators were only known close to the boundary of $AdS_5$ 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 $AdS_5 \times S^5$ string amplitudes.