  In this letter we follow up recent work of Halverson-Kumar-Morrison on some
exotic examples of gauged linear sigma models (GLSM's). Specifically, they
describe a set of U(1) x Z_2 GLSM's with superpotentials that are quadratic in
p fields, rather than linear as is typically the case. These theories RG flow
to sigma models on branched double covers, where the double cover is realized
via a Z_2 gerbe. For that gerbe structure, and hence the double cover, the Z_2
factor in the gauge group is essential. In this letter we propose an analogous
geometric understanding of phases without that Z_2, in terms of Ricci-flat (but
not Calabi-Yau) stacks which look like Fano manifolds with hypersurfaces of Z_2
orbifolds.
