Harmonic Superspace from the $AdS_5\times S^5$ Pure Spinor Formalism

TL;DR

This paper develops a method to describe supergravity vertex operators in an $AdS_5\times S^5$ background using pure spinor formalism and harmonic superspace, providing explicit superfield expressions near the boundary.

Contribution

It introduces a new approach combining pure spinor formalism with harmonic superspace to compute supergravity vertex operators in $AdS_5\times S^5$.

Findings

Explicit superfield expressions for vertex operators near the boundary.

Cohomology computed using harmonic superspace variables.

Bridging pure spinor formalism with harmonic superspace techniques.

Abstract

On-shell supergravity vertex operators in an $AdS_5\times S^5$ background are described in the pure spinor formalism by the zero mode cohomology of a BRST operator. After expanding the pure spinor BRST operator in terms of the $AdS_5$ radius variable, this cohomology is computed using N=4 harmonic superspace variables and explicit superfield expressions are obtained for the behavior of supergravity vertex operators near the boundary of $AdS_5$.