Invariance of the coherent master-space component under toric Seiberg duality

Let two quiver gauge theories be related by toric Seiberg duality, and let ${}^{{\rm Irr}}\!{\cal F}^{\flat}$ denote the coherent component of the master space of a theory.

Coherent-component invariance conjecture. Quivers which are toric (Seiberg) duals have the same coherent component of the master space.

The conjecture proposes that the top-dimensional component of the F-term variety is an invariant of the toric Calabi–Yau singularity rather than of a particular toric phase. The paper supports it through explicit examples, but gives no general proof.