Spin-cobordisms, surgeries and fermionic modular bootstrap

Understand

We consider general fermionic quantum field theories with a global finite group symmetry $G$, focusing on the case of 2-dimensions and torus spacetime.

• The modular transformation properties of the family of partition functions with different backgrounds is determined by the 't Hooft anomaly of $G$ and fermion parity.
• For a general possibly non-abelian $G$ we provide a method to determine the modular transformations directly from the bulk 3d invertible topological quantum field theory (iTQFT) corresponding to the anomaly by inflow.
• We also describe a method of evaluating the character map from the real representation ring of $G$ to the group which classifies anomalies.