Scattering Amplitudes and form factors at Strong Coupling

• Alday and Maldacena showed that scattering amplitudes in N=4 SYM may be computed at strong coupling using the so-called gauge/string duality, where the problem was reduced to a string minimal surface problem in a special curved spacetime (see paper). This non-trivial geometrical problem was later solved in a series of papers by Alday, Maldacena and collaborators, where the integrability of the classical world-sheet theory played an essential role (see e.g. paper). I showed the four-cusp solution was unique after imposing the Virasoro constraints, which solved a puzzle in the literature. I also developed a method to compute strong coupling amplitudes in the subtle case where the number of gluons is a multiple of four in AdS5 background. (See our paper, paper and paper.)

Amplitudes  v.s.  Minimal surface

• With Zhi-Quan Gao, I also studied form factors at strong coupling via AdS/CFT duality and integrability, where the Y-system for form factors in AdS5 was constructed and the insertions of multiple operators were also considered. This work was initially inspired by the coincidence between N=4 SYM and QCD at two-loop three-point. If the two-loop coincidence is true for higher loops, one may expect the strong coupling form factors would carry a non-trivial piece of information of strong coupling QCD. While the AdS3 case has been understood, one needs to go to AdS5 to study the three-point case. It turns out that the monodromy associated to the operator is more complicated and the main challenge is to truncate the integrable system in a conformal invariant way and also to extract the answer (the area) from the integrable system. Another interesting problem is to study the multi-operator insertions which may be connected to correlation functions at strong coupling. It turns out that one could make similar truncations for such cases. (See our paper for more details.)