Open-closed superstring amplitudes using vertex operators in $\mathrm{AdS}_5 \times \mathrm{S}^5$

Using the pure spinor formalism, a particular superstring scattering amplitude involving one closed string and $N$ open string vertex operators in $\mathrm{AdS}{}_5 \times \mathrm{S}^5$ is studied. It is shown that the tree-level amplitude containing one supergravity state and $N$ super-Yang-Mills states located on D3-branes near the AdS${}_5$ boundary can be expressed as a $d=4$ ${\cal N}=4$ harmonic superspace integral in terms of the supergravity and super-Yang-Mills superfields.