Hamiltonian flow between standard module Lagrangians
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911352039145472 |
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| author | Tong, Yujin |
| author_facet | Tong, Yujin |
| contents | In Aganagic's Fukaya category of the Coulomb branch of quiver gauge theory, the $T_θ$-brane algebra gives a symplectic realization of the Khovanov-Lauda-Rouquier-Webster (KLRW) algebra, where each standard module is known to admit two Lagrangian realizations: the 'U'-shaped $T$-brane and the step $I$-brane. We show that the latter arises as the infinite-time limit of the Hamiltonian evolution of the former, thus serving as a generalized thimble. This provides a geometric realization of the categorical isomorphism previously established through holomorphic disc counting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian flow between standard module Lagrangians Tong, Yujin Symplectic Geometry High Energy Physics - Theory Quantum Algebra In Aganagic's Fukaya category of the Coulomb branch of quiver gauge theory, the $T_θ$-brane algebra gives a symplectic realization of the Khovanov-Lauda-Rouquier-Webster (KLRW) algebra, where each standard module is known to admit two Lagrangian realizations: the 'U'-shaped $T$-brane and the step $I$-brane. We show that the latter arises as the infinite-time limit of the Hamiltonian evolution of the former, thus serving as a generalized thimble. This provides a geometric realization of the categorical isomorphism previously established through holomorphic disc counting. |
| title | Hamiltonian flow between standard module Lagrangians |
| topic | Symplectic Geometry High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2511.06431 |