Abstract
We generalize Coulomb-branch-based gauged linear sigma model (GLSM)–computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the low energy limit of the GLSM is a pure Coulomb branch, and quantum cohomology is determined by the critical locus of a twisted one-loop effective superpotential. We extend these results to cases for which the low energy limit of the GLSM includes both Coulomb and Higgs branches, where the latter is a Landau-Ginzburg orbifold. We describe the state spaces and products of corresponding operators in detail, comparing a geometric phase description, where the operator product ring is quantum cohomology, to the description in terms of Coulomb and Higgs branch states. As a concrete test of our methods, we compare to existing mathematics results for quantum cohomology rings of hypersurfaces in projective spaces.
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Acknowledgments
We would like to thank J. Knapp, L. Mihalcea, W. Xu, H. Zhang, and H. Zou for useful discussions. I.V.M. was partially supported by the Humboldt Research Award and the Jean d’Alembert Program at the University of Paris-Saclay, as well as the Educational Leave program at James Madison University. Part of this work was carried out while I.V.M. was visiting the Albert Einstein Institute (Max Planck Institute for Gravitational Physics) as well as LPTHE at Sorbonne Université, UPMC Paris 06, and he is grateful to both AEI and LPTHE for their generous hospitality. E.S. was partially supported by NSF grant PHY- 2014086. We are also grateful to the Simons Center for Geometry and Physics for hospitality and support during the workshop GLSM@30, where some of this work was carried out.
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Gu, W., Melnikov, I.V. & Sharpe, E. Quantum cohomology from mixed Higgs-Coulomb phases. J. High Energ. Phys. 2024, 10 (2024). https://doi.org/10.1007/JHEP02(2024)010
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DOI: https://doi.org/10.1007/JHEP02(2024)010