On the Lefschetz thimbles structure of the Thirring model

Understand

The complexification of field variables is an elegant approach to attack the sign problem.

• In one approach one integrates on Lefschetz thimbles: over them, the imaginary part of the action stays constant and can be factored out of the integrals so that on each thimble the sign problem disappears.
• However, for systems in which more than one thimble contribute one is faced with the challenging task of collecting contributions coming from multiple thimbles.
• The Thirring model is a nice playground to test multi-thimble integration techniques; even in a low dimensional theory, the thimble structure can be rich.