Noncommutative resolutions and CICY quotients from a non-Abelian GLSM, by Johanna Knapp, Joseph McGovern
Summarize this article with:
SciPost Physics Home Authoring Refereeing Submit a manuscript About Noncommutative resolutions and CICY quotients from a non-Abelian GLSM Johanna Knapp, Joseph McGovern SciPost Phys. 19, 156 (2025) · published 17 December 2025 doi: 10.21468/SciPostPhys.19.6.156 pdf BiBTeX RIS Submissions/Reports Abstract We discuss a one-parameter non-Abelian GLSM with gauge group $(U(1)× U(1)× U(1))\rtimes\mathbb{Z}_3$ and its associated Calabi-Yau phases. The large volume phase is a free $\mathbb{Z}_3$-quotient of a codimension $3$ complete intersection of degree-$(1,1,1)$ hypersurfaces in $\mathbb{P}^2×\mathbb{P}^2×\mathbb{P}^2$. The associated Calabi-Yau differential operator has a second point of maximal unipotent monodromy, leading to the expectation that the other GLSM phase is geometric as well. However, the associated GLSM phase appears to be a hybrid model with continuous unbroken gauge symmetry and cubic superpotential, together with a Coulomb branch. Using techniques from topological string theory and mirror symmetry we collect evidence that the phase should correspond to a non-commutative resolution, in the sense of Katz-Klemm-Schimannek-Sharpe, of a codimension two complete intersection in weighted projective space with $63$ nodal points, for which a resolution has $\mathbb{Z}_3$-torsion. We compute the associated Gopakumar-Vafa invariants up to genus $11$, incorporating their torsion refinement. We identify two integral symplectic bases constructed from topological data of the mirror geometries in either phase. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.19.6.156TI - Noncommutative resolutions and CICY quotients from a non-Abelian GLSMPY - 2025/12/17UR - https://scipost.org/SciPostPhys.19.6.156JF - SciPost PhysicsJA - SciPost Phys.VL - 19IS - 6SP - 156A1 - Knapp, JohannaAU - McGovern, JosephAB - We discuss a one-parameter non-Abelian GLSM with gauge group $(U(1)× U(1)× U(1))\rtimes\mathbb{Z}_3$ and its associated Calabi-Yau phases. The large volume phase is a free $\mathbb{Z}_3$-quotient of a codimension $3$ complete intersection of degree-$(1,1,1)$ hypersurfaces in $\mathbb{P}^2×\mathbb{P}^2×\mathbb{P}^2$. The associated Calabi-Yau differential operator has a second point of maximal unipotent monodromy, leading to the expectation that the other GLSM phase is geometric as well. However, the associated GLSM phase appears to be a hybrid model with continuous unbroken gauge symmetry and cubic superpotential, together with a Coulomb branch. Using techniques from topological string theory and mirror symmetry we collect evidence that the phase should correspond to a non-commutative resolution, in the sense of Katz-Klemm-Schimannek-Sharpe, of a codimension two complete intersection in weighted projective space with $63$ nodal points, for which a resolution has $\mathbb{Z}_3$-torsion. We compute the associated Gopakumar-Vafa invariants up to genus $11$, incorporating their torsion refinement. We identify two integral symplectic bases constructed from topological data of the mirror geometries in either phase.ER - × @Article{10.21468/SciPostPhys.19.6.156, title={{Noncommutative resolutions and CICY quotients from a non-Abelian GLSM}}, author={Johanna Knapp and Joseph McGovern}, journal={SciPost Phys.}, volume={19}, pages={156}, year={2025}, publisher={SciPost}, doi={10.21468/SciPostPhys.19.6.156}, url={https://scipost.org/10.21468/SciPostPhys.19.6.156},} Ontology / Topics See full Ontology or Topics database. Calabi-Yau manifolds Gauge theory Authors / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Johanna Knapp, 1 Joseph McGovern 1 University of Melbourne [UniMelb] Funders for the research work leading to this publication Australian Research Council [ARC] Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG] University of Melbourne [UniMelb]