Supersymmetric Quantum Field Theory
The members of our group have played a pioneering role in the efforts to understand the observables in highly supersymmetric theories. We have a strong
focus on the extraordinarly rich N = 4 super Yang-Mills theories, for which observables such as scattering amplitudes, Wilson loops, and correlation functions of local operators can be analytically computed to high (and sometimes arbitrarily large) order in the coupling. This stems largely from the exceptional integrability properties of the four-dimensional N = 4 SYM theories, which normally arises only in two-dimensional QFTs. Our research focuses on N = 4 SYM as an important toy model for understanding QFT and quantum gravity more generally. The power of this approach is clearly demonstrated by many past results, for example many modern methods for computing scattering amplitudes in the Standard Model were first discovered and developed in N = 4 SYM. It is essential to continue developing such techniques in order to analyze future data from particle colliders like the LHC. We also investigate whether and to what extent these ideas can be extended beyond the planar limit and to more realistic models. We have already made substantial progress in this direction, for example through the development of ambitwistor string models which describe 4d gauge and gravity theories with any amount of supersymmetry. Furthermore, several techniques developed for the bootstrap analysis of the N = 4 theories have already been used for other theories.
Our research sits at the intersection of three exceptionally active topics of current research – Amplitudes, Integrability, Bootstrap. These three by now intimately related topics have brought together people from a wide range of other fields, ranging from number theory to computer science to LHC phenomenology.