Quantization commutes with reduction for coisotropic A-branes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911684668424192 |
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| author | Leung, Naichung Conan Xie, Ying Yau, Yutung |
| author_facet | Leung, Naichung Conan Xie, Ying Yau, Yutung |
| contents | On a Hamiltonian $G$-manifold $X$, we define the notion of $G$-invariance of coisotropic A-branes $B$. Under neat assumptions, we give a Marsden-Weinstein-Meyer type construction of a coisotropic A-brane $B_{\operatorname{red}}$ on $X // G$ from $B$, recovering the usual construction when $B$ is Lagrangian. For a canonical coisotropic A-brane $B_{\operatorname{cc}}$ on a holomorphic Hamiltonian $G_\mathbb{C}$-manifold $X$, there is a fibration of $(B_{\operatorname{cc}})_{\operatorname{red}}$ over $X // G_\mathbb{C}$.
We also show that `intersections of A-branes commute with reduction'. When $X = T^*M$ for $M$ being compact Kähler with a Hamiltonian $G$-action, Guillemin-Sternberg `quantization commutes with reduction' theorem can be interpreted as $\operatorname{Hom}_{X // G}(B_{\operatorname{red}}, (B_{\operatorname{cc}})_{\operatorname{red}}) \cong \operatorname{Hom}_X(B, B_{\operatorname{cc}})^G$ with $B = M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantization commutes with reduction for coisotropic A-branes Leung, Naichung Conan Xie, Ying Yau, Yutung Symplectic Geometry Mathematical Physics Differential Geometry On a Hamiltonian $G$-manifold $X$, we define the notion of $G$-invariance of coisotropic A-branes $B$. Under neat assumptions, we give a Marsden-Weinstein-Meyer type construction of a coisotropic A-brane $B_{\operatorname{red}}$ on $X // G$ from $B$, recovering the usual construction when $B$ is Lagrangian. For a canonical coisotropic A-brane $B_{\operatorname{cc}}$ on a holomorphic Hamiltonian $G_\mathbb{C}$-manifold $X$, there is a fibration of $(B_{\operatorname{cc}})_{\operatorname{red}}$ over $X // G_\mathbb{C}$. We also show that `intersections of A-branes commute with reduction'. When $X = T^*M$ for $M$ being compact Kähler with a Hamiltonian $G$-action, Guillemin-Sternberg `quantization commutes with reduction' theorem can be interpreted as $\operatorname{Hom}_{X // G}(B_{\operatorname{red}}, (B_{\operatorname{cc}})_{\operatorname{red}}) \cong \operatorname{Hom}_X(B, B_{\operatorname{cc}})^G$ with $B = M$. |
| title | Quantization commutes with reduction for coisotropic A-branes |
| topic | Symplectic Geometry Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2506.06859 |