A few Ricci-flat stacks as phases of exotic GLSMʼs

In this Letter we follow up the recent work of Halverson, Kumar and Morrison on some exotic examples of gauged linear sigma models (GLSMʼs). Specifically, they describe a set of U(1)×Z2 GLSMʼs 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 Z2 gerbe. For that gerbe structure, and hence the double cover, the Z2 factor in the gauge group is essential. In this Letter we propose an analogous geometric understanding of phases without that Z2, in terms of Ricci-flat (but not Calabi-Yau) stacks which look like Fano manifolds with hypersurfaces of Z2 orbifolds.