Defects and non-perturbative operators in superconformal theories

• Applicants: Professorin Dr. Ilka Brunner; Professor Dr. Peter Mayr
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 336983122

The main research direction of the current proposal is the investigation of novel structures in particularly simple quantum field theories. The focus is on theories which allow to obtain exact results that go beyond perturbation theory. A class of theories that offers such simplifcations are supersymmetric quantum field theories, where we can make use of new results on the computation of path integrals and correlation functions. The structures that we want to investigate further in the second half of the proposal are extended objects of different dimensions. Examples are line defects (such as Wilson lines) or higher dimensional surface defects. We are particularly interested in quantum field theories in 2 and 3 dimensions. The case of 2 dimensions is of interest in the context of string theory, the 3 dimensional case provides on the one hand a quantization of certain two dimensional results. On the other hand it is of interest, because there are many interesting classes of examples (e.g. Rozansky Witten theory, linear sigma models). In the current proposal we can build upon results in phase 1, which contain in particular investigations on boundary conditions and line defects in 3d N=2 theories and renormalization group flows in 2d N=(2,2) theories. We plan to extend and deepen these results. Here, we plan to relate different theories using defects. This can be achieved by so-called generalized orbifold constructions. In those, the basic idea is to define new ideas from old ones using triangulations and defect networks. In this context, we plan to study 3 dimensional theories, since orbifold constructions are not much explored in higher dimensions. As a further focus are, we plan to continue our investigations of spaces of quantum field theories and flows between supersymmetric quantum fields theories. Here, defects are used to connect different theories and properties of defects are used to quantify relations between theories.

• DFG Programme: Research Grants