Extended field theories and index theory

An anomaly is the breaking of a classical symmetry under quantization. Following a proposal by D. Freed, a quantum field theory with anomaly can be described by a field theory relative to an extended field theory in one space-time dimension higher. All information about the anomaly is contained in this extended field theory.
The goal of this project is to study anomalies in condensed matter systems and string theory using extended field theories. This point of view allows the use of elaborate mathematical methods from (higher) category theory, gerbe theory and algebraic topology in this context. By using these methods we hope to produce new insights into the physics of the studied systems.