A few Ricci-flat stacks as phases of exotic GLSM's

TL;DR

This paper explores exotic phases of gauged linear sigma models (GLSMs) that lead to Ricci-flat stacks resembling Fano manifolds with Z_2 orbifold hypersurfaces, expanding geometric understanding beyond Calabi-Yau cases.

Contribution

It introduces a geometric interpretation of GLSM phases without Z_2 gauge factors, describing Ricci-flat stacks as Fano-like structures with orbifold hypersurfaces.

Findings

Identifies Ricci-flat stacks as phases of GLSMs without Z_2 gauge symmetry.

Connects these stacks to Fano manifolds with orbifold hypersurfaces.

Provides a new geometric framework for non-Calabi-Yau GLSM phases.

Abstract

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.