Higher-point functions and integrability

In quantum field theory in four dimensions, calculations can often only be done by perturbation theory in the coupling constant. In QED the coupling is small, so this series expansion is helpful. Yet, e.g. in QCD at low energy this is not the case. On the other hand, many two-dimensional systems are integrable, i.e they can be solved exactly at generic coupling.

We aim at the development of non-perturbative methods in four-dimensional QFT utilising integrability. We propose studying the so-called N=4 super Yang-Mills theory, a cousin of QCD. The strong coupling limit of the model is described by a string theory. The calculation of the energy levels/anomalous dimensions of this ``AdS/CFT correspondence'' has been described by an integrable model.

Current work is concerned with integrable structures controlling higher-point objects. In particular, we wish to develop the idea of tiling n-point correlation functions by elementary patches fixed by symmetry.