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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.07624 |
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| _version_ | 1866914904707956736 |
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| author | Cheng, Shi |
| author_facet | Cheng, Shi |
| contents | We try to give a geometric construction for 3d $\mathcal{N}=2$ gauge theories using three-manifolds and Dehn surgeries. We follow the story that wrapping M5-branes on plumbing three-manifolds leads to 3d theories with mixed Chern-Simons levels. This construction can be decorated by adding non-compact Lagrangian submanifolds in the cotangent bundles of three-manifolds. The M5-branes wrapping on these submanifolds through M-theory/IIB string duality lead to flavor D5-branes that engineer chiral multiplets. In this note, we only consider unknotted matter circles, which are intersections between these non-compact M5-branes and plumbing manifolds. Then various dualities of 3d theories can be interpreted as Kirby moves and equivalent surgeries. We also find the dictionary between geometric structures of three-manifolds and physical aspects of gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07624 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Surgery and Matter for 3d Theories Cheng, Shi High Energy Physics - Theory Geometric Topology We try to give a geometric construction for 3d $\mathcal{N}=2$ gauge theories using three-manifolds and Dehn surgeries. We follow the story that wrapping M5-branes on plumbing three-manifolds leads to 3d theories with mixed Chern-Simons levels. This construction can be decorated by adding non-compact Lagrangian submanifolds in the cotangent bundles of three-manifolds. The M5-branes wrapping on these submanifolds through M-theory/IIB string duality lead to flavor D5-branes that engineer chiral multiplets. In this note, we only consider unknotted matter circles, which are intersections between these non-compact M5-branes and plumbing manifolds. Then various dualities of 3d theories can be interpreted as Kirby moves and equivalent surgeries. We also find the dictionary between geometric structures of three-manifolds and physical aspects of gauge theories. |
| title | Surgery and Matter for 3d Theories |
| topic | High Energy Physics - Theory Geometric Topology |
| url | https://arxiv.org/abs/2310.07624 |