Evolution equations for composite operators and AdS/CFT integrability

Quantum field theory gives an excellent description for the electromagnetic, weak, and strong fundamental interactions by means of perturbative expansions in the coupling constant. It allows to obtain results that can be compared to experiments. In many cases large logarithms appear in perturbative calculations. These should then be summed exactly, i.e. to all orders in perturbation theory. The arising evolution equations are widely used for the theoretical description of high energy scattering processes, which are extensively studied at the LHC and in other experiments at colliders. During forty years of investigations many remarkable properties related to these evolution equations were found. In particular, an important connection between high-energy scattering and certain exactly solvable two-dimensional field-theoretical models was discovered. A similar integrability phenomenon was discovered in the investigation of composite operators in the planar limit of the famous AdS/CFT correspondence. In this project it is planned to extend the investigations of integrability to other evolution equations in the framework of the planar gauge/string duality and beyond the planar limit within the collaboration between the applicant, Dr. Vitaly Velizhanin, an expert in the considered evolution equations, and the research group "Mathematical Physics of Space, Time and Matter" at Humboldt University, which focuses among other things on AdS/CFT integrability. It is planned to calculate the higher-loop anomalous dimensions of composite operators and to study their properties. The obtained results will then be used for testing current approaches and for developing new methods.