Gluon scattering in N=4 super Yang-Mills at finite temperature

We extend the AdS/CFT prescription of Alday and Maldacena to finite temperature T, defining an amplitude for gluon scattering in N = 4 Super Yang-Mills at strong coupling frond string theory. It is defined by a lightlike "Wilson loop" living at the horizon of the T-dual to the black hole in AdS space. Unlike the zero temperature case; this is different from the Wilson loop contour defined at the boundary of the AdS black hole metric. Thus at nonzero T there is no relation between gluon scattering amplitudes and the Wilson loop. We calculate a, gauge theory observable that can be interpreted as the amplitude at strong coupling for forward scattering of a low energy gluon (E < T) off a high energy gluon (E >> T) in both cutoff and generalized dimensional regularization. The generalized dimensional regularization is defined in string theory as an IR modified dimensional reduction. For this calculation, the corresponding usual Wilson loop of the same boundary shape was argued to be related to the jet quenching parameter of the finite temperature N = 4 SYM plasma, while the gluon scattering amplitude is related to the viscosity coefficient.