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

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.

14 pages, LaTeX; v2: typos corrected

References in corpus (6)

• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Notes on gauging noneffective group actions
• GLSM's for partial flag manifolds
• New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
• The Stringy Instanton Partition Function
• Homological Projective Duality via Variation of Geometric Invariant Theory Quotients

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• Categorical Equivalence and the Renormalization Group
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• Decomposition in Chern-Simons theories in three dimensions
• Global aspects of moduli spaces of 2d SCFTs