Amplitudes - our main goals

 

  • Exploration of the amplitude/Wilson loop duality and various symmetries that arise in this context, such as dual superconformal and Yangian symmetries.
  • Understanding the geometric nature of Feynman integrals for amplitudes and their relation to integrability.
  • Finding exact non-perturbative equations/expressions for the SYM amplitudes.
  • Relating these results to QCD amplitudes.
  • Going beyond MHV amplitudes at strong coupling.
  • Quantization of the stringy Y-system equations for light-like Wilson loops.


Strong coupling. The construction of amplitudes at strong coupling boils down to finding the free energy of an auxiliary quantum integrable system involving a family of Y-functions, similar to but not the same as those that arose in the study of the spectral problem. This system of equations can be analyzed by practically the same methods. Our research in this direction will profit from years of numerical and analytical experience with TBA equations, most notably in the Saclay and Durham groups.

 

Weak coupling. Progress in understanding amplitudes largely relied upon the triality of amplitudes, Wilson loops and correlation functions. We are planning to further develop perturbative methods to calculate amplitudes in N = 4 SYM and beyond and to get insights
into the nonperturbative relation between amplitudes, Wilson loops and correlation functions.

 

Hidden symmetries. Physically, perhaps the most important outcome of the proposed Wilson loop representation of the scattering amplitudes is the realization that the Wilson loops possess a so-called dual conformal symmetry. The algebraic completion of this symmetry combined with the ordinary conformal invariance generates an infinite dimensional symmetry algebra called the ╩╗Yangian╩╝ that often arises in integrable systems. This observation opens an avenue for application of integrability methods that has been successfully used for the spectral problem, for scattering amplitudes.