We will investigate the relations between three-dimensional topological field theories and two-dimensional conformal field theories when the representation categories are not semisimple, with a particular focus on the resulting derived structures. This can be used to study relations between N=4, d=3 supersymmetric QFT and vertex algebras recently discovered in theoretical physics. We will investigate how derived structures of vertex algebra representation categories encode the geometry of the moduli spaces of vacua of the SUSY QFTs in this context.
DFG Programme
Collaborative Research Centres
