Hidden topological angles and Lefschetz thimbles

Understand

We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems.

• HTAs are distinct from theta-parameters in the lagrangian.
• They arise as invariant angle associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles).
• Physical effects of HTAs become most transparent upon analytic continuation in $n_f$ to non-integer number of flavors, reducing in the integer $n_f$ limit to a $\mathbb Z_2$ valued phase difference between dominant saddles.