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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.12334 |
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| _version_ | 1866909090513420288 |
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| author | Gu, W. Melnikov, I. V. Sharpe, E. |
| author_facet | Gu, W. Melnikov, I. V. Sharpe, E. |
| contents | We generalize Coulomb-branch-based gauged linear sigma model (GLSM)-based computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the IR phase of the GLSM is a pure Coulomb branch, and quantum cohomology is determined by the critical locus of a twisted one-loop effective superpotential. Here, we systematically extend to cases for which the IR phase is a mixture of 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 OPE ring is quantum cohomology, to the IR 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 in numerous examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum cohomology from mixed Higgs-Coulomb branches Gu, W. Melnikov, I. V. Sharpe, E. High Energy Physics - Theory We generalize Coulomb-branch-based gauged linear sigma model (GLSM)-based computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the IR phase of the GLSM is a pure Coulomb branch, and quantum cohomology is determined by the critical locus of a twisted one-loop effective superpotential. Here, we systematically extend to cases for which the IR phase is a mixture of 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 OPE ring is quantum cohomology, to the IR 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 in numerous examples. |
| title | Quantum cohomology from mixed Higgs-Coulomb branches |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2308.12334 |