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Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties. (English) Zbl 1397.81378
Summary: The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi-Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models – which we refer to as the PAX and the PAXY model – are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.

MSC:
81T60 Supersymmetric field theories in quantum mechanics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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