The main goal of my proposed research is to develop new methods to study superconformal field theories (SCFT) that fully exploit their symmetries and hidden structures. In recent years enormous progress has been made in our understanding of different aspects of such theories but it is rather clear that many new fundamental results can be obtained in the near future. My research programme can be organised in two main strands that I will briefly describe. The first direction is to study the coupling constant dependence of correlation functions in the maximally super-symmetric Yang-Mills theory in four dimensions, namely N=4 SYM. To address this challenging problem I will use the method of conformal perturbation theory combined with constraints from the self-duality properties of N=4 SYM with respect to modular transformations of the complexified gauge coupling. It should be remarked that this programme concerns N=4 SYM with a fixed, finite dimensional, gauge group, e.g. SU(2), but it can also make contact with the planar limit in which a lot more is known thanks to the emergent integrable structure. Additional inputs from results obtained using supersymmetric localization and the modern numerical bootstrap will be of vital importance. The second direction is to explore a remarkable connection between four dimensional N=2 SCFTs and Vertex Operator Algebras (VOAs). The main goals are to understand specific examples in great details but also tackle the outstanding question of classifying 4d N=2 SCFTs by looking at them through VOA lenses. A crucial tool that will be used is a novel free-field construction of such VOAs that I have recently introduced together with C. Beem and L. Rastelli.

Carlo Meneghelli– INFN MILANO BICOCCA Gr. Collegato di Parma

Carlo Meneghelli is a researcher at INFN Parma Unit. He received his PhD from Humboldt University of Berlin in 2011 followed by postdoctoral positions at Fachbereich Mathematik/DESY Theory Group, Hamburg, the Simons Center for Geometry and Physics at Stony Brook University and the Mathematical Institute at the University of Oxford. His research focuses on mathematical aspects of quantum field theory. For the past few years, he has been working on applying bootstrap methods in the context of super-conformal field theories. He is also interested in integrable models and their relations with super-symmetric gauge theories.