Massive quark scattering at strong coupling from AdS/CFT

TL;DR

This paper extends the AdS/CFT framework to compute gluon and quark scattering amplitudes at strong coupling, incorporating massive quarks via D7-branes and deriving exact string worldsheets for these processes.

Contribution

It introduces a method to include massive quarks in strong coupling scattering amplitude calculations using AdS/CFT, generalizing previous massless gluon results.

Findings

Derived boundary conditions for massive particles in string worldsheets.

Obtained exact worldsheets for quark-quark and quark-gluon scattering.

Showed that massive quark amplitudes reduce to massless gluon results when quark mass approaches zero.

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 N=2 hypermultiplets which arise when D7-brane probes are included in the AdS_5 x S^5 geometry. We work in the quenched approximation, treating the N=2 matter multiplets as external sources coupled to the N=4 SYM fields. We first derive appropriate massive-particle boundary conditions for the string scattering worldsheets. We then find an exact worldsheet 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 worldsheet and amplitude for the scattering of four massive quarks. Our worldsheet 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.