Quivers and BPS states in 3d and 4d
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910178279948288 |
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| author | Kucharski, Piotr Longhi, Pietro Noshchenko, Dmitry Park, Sunghyuk Sułkowski, Piotr |
| author_facet | Kucharski, Piotr Longhi, Pietro Noshchenko, Dmitry Park, Sunghyuk Sułkowski, Piotr |
| contents | We propose a symmetrization relation between BPS quivers encoding 4d $\mathcal{N}=2$ theories and symmetric quivers associated to 3d $\mathcal{N}=2$ theories. We analyse in detail the symmetrization of BPS quivers for a series of $A_m$ Argyres-Douglas theories by engineering 3d-4d systems in geometric backgrounds involving appropriate 3-manifolds and Riemann surfaces. We discuss properties of these geometric backgrounds and derive the corresponding quiver partition functions from the perspective of skein modules, which forms the foundation of the symmetrization map for the minimal chamber. We also prove that the structure of wall-crossing in 4d $A_m$ Argyres-Douglas theories is isomorphic to the structure of unlinking of symmetric quivers encoding their partner 3d theories, which allows for a proper definition of the symmetrization map outside the minimal chamber. Finally, we show that the Schur indices of 4d theories are captured by symmetric quivers that include symmetrization of 4d BPS quivers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quivers and BPS states in 3d and 4d Kucharski, Piotr Longhi, Pietro Noshchenko, Dmitry Park, Sunghyuk Sułkowski, Piotr High Energy Physics - Theory Mathematical Physics Combinatorics Geometric Topology Quantum Algebra We propose a symmetrization relation between BPS quivers encoding 4d $\mathcal{N}=2$ theories and symmetric quivers associated to 3d $\mathcal{N}=2$ theories. We analyse in detail the symmetrization of BPS quivers for a series of $A_m$ Argyres-Douglas theories by engineering 3d-4d systems in geometric backgrounds involving appropriate 3-manifolds and Riemann surfaces. We discuss properties of these geometric backgrounds and derive the corresponding quiver partition functions from the perspective of skein modules, which forms the foundation of the symmetrization map for the minimal chamber. We also prove that the structure of wall-crossing in 4d $A_m$ Argyres-Douglas theories is isomorphic to the structure of unlinking of symmetric quivers encoding their partner 3d theories, which allows for a proper definition of the symmetrization map outside the minimal chamber. Finally, we show that the Schur indices of 4d theories are captured by symmetric quivers that include symmetrization of 4d BPS quivers. |
| title | Quivers and BPS states in 3d and 4d |
| topic | High Energy Physics - Theory Mathematical Physics Combinatorics Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2508.09729 |