2025/04/08 by Johanna Knapp, Knapp, Johanna, Joseph McGovern +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2504.06147
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
We discuss a one-parameter non-abelian GLSM with gauge group (U(1)× U(1)× U(1))\rtimesℤ3 and its associated Calabi-Yau phases. The large volume phase is a free ℤ3-quotient of a codimension 3 complete intersection of degree-(1,1,1) hypersurfaces in ℙ2×ℙ2×ℙ2. 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 ℤ3-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.