U(1) spin Chern-Simons theory and Arf invariants in two dimensions

Understand

The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd.

• Its dynamics is captured by the 2d CFT of a compact boson with a certain radius.
• Recently it was recognized that a dependence on the 2d spin structure can be given to the CFT by modifying it using the so-called Arf invariant.
• We demonstrate that one can reorganize the torus partition function of the modified CFT into a finite sum involving a finite number of conformal blocks.