Massive quark scattering at strong coupling from AdS/CFT

Abstract

We extend the analysis of Alday and Maldacena for obtaining gluon scattering amplitudes at strong coupling to include external massive quark states. Our quarks are actually the $\mathcal{N}=2$ hypermultiplets which arise when $D7$-brane probes are included in the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ geometry. We work in the quenched approximation, treating the $\mathcal{N}=2$ matter multiplets as external sources coupled to the $\mathcal{N}=4$ supersymmetric Yang-Mills fields. We first derive appropriate massive-particle boundary conditions for the string scattering world sheets. We then find an exact world sheet which corresponds to the scattering of two massive quarks and two massless gluons and extract from this the associated scattering amplitude. We also find the world sheet and amplitude for the scattering of four massive quarks. Our world sheet solutions reduce to the four massless gluon solution of Alday and Maldacena in the limit of zero quark mass. The amplitudes we compute can also be interpreted in terms of 2-2 scattering involving gluons and massive $W$ bosons.