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We record an observation about the Witten indices in two families of gaugedlinear sigma models: the U(2) model for linear sections of Grassmannians, andthe U(1) model for quadric complete intersections. We describe how the Wittenindices are related to the Euler characteristics of the singular skew-symmetricor symmetric determinantal varieties featuring in the analysis of theiropposite phases, and we discuss the extent to which these relationships can bereconciled with standard Born-Oppenheimer arguments.

Two-dimensional gauge dynamics and the topology of singular determinantal varieties