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 AdS5 × S5 background. Previously, the vertex operators were only known close to the boundary of AdS5 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 AdS5 × S5 string amplitudes.
Highlights
AdS5 [8] and they were used to compute open-closed string amplitudes in [9, 10] reproducing the expected holographic results
In any type II superstring background, the supergravity vertex operators in the pure spinor formalism are described by a gauge superfield
We argue that the picture raising procedure is well defined in AdS5 × S5, that our results reduce correctly to the well known dilaton vertex operator in an appropriate limit and that the vertices have the correct flat space limit
Summary
We review the known massless vertex operators in a flat background. In particular, we explain their recent minus eight picture realizations. With (V−7)a1...a7 anti-symmetric in all its indices This follows because the BRST operator is nilpotent and it trivially annihilates the delta functions. In order for the BRST operator to be nilpotent, and the theory well defined, the variables λ’s have to satisfy several quadratic constraints, the so called pure spinor constraints. In AdS, the calculation is complicated by the fact that the λ’s are not BRST invariant, see (3.8), and the transformations of the remaining worldsheet variables have many terms. We believe that the easiest way of obtaining the vertex operators for any alternative cosets is to generate a basis of invariants and solving the condition of BRST closeness by numerically fitting for the coefficients of the basis. It is possible to write a second basis and verify that the obtained vertex is not BRST exact
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