Relation between IDB and KSW thimble truncation

Determine whether the cropping of Lefschetz thimbles imposed by the imaginary distance bound is a distinct manifestation of the same underlying mechanism as the cropping caused by the Kontsevich–Segal–Witten non-allowability condition.

Background

The paper compares two restrictions on Lefschetz thimbles in the complex axion-separation and covering-lapse planes. Imposing the imaginary distance bound truncates steepest-descent flowlines outside the allowed strip, while the Kontsevich–Segal–Witten criterion similarly removes portions of thimbles that enter the region of non-allowable complex metrics.

The authors observe that these truncation phenomena resemble one another but do not establish that they arise from a common underlying mechanism. The unresolved problem is therefore to determine whether the imaginary-distance-bound restriction and KSW-based restriction are manifestations of the same structural principle in the gravitational path integral.