S-dual of Hamiltonian $\mathbf G$ spaces and relative Langlands duality
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917772304318464 |
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| author | Nakajima, Hiraku |
| author_facet | Nakajima, Hiraku |
| contents | The S-dual $(\mathbf G^\vee\curvearrowright\mathbf M^\vee)$ of the pair $(\mathbf G\curvearrowright\mathbf M)$ of a smooth affine algebraic symplectic manifold $\mathbf M$ with hamiltonian action of a complex reductive group $\mathbf G$ was introduced implicitly in [arXiv:1706.02112] and explicitly in [arXiv:1807.09038] under the cotangent type assumption. The definition was a modification of the definition of Coulomb branches of gauge theories in [arXiv:1601.03586]. It was motivated by the S-duality of boundary conditions of 4-dimensional $\mathcal N=4$ super Yang-Mills theory, studied by Gaiotto and Witten [arXiv:0807.3720]. It is also relevant to the relative Langlands duality proposed by Ben-Zvi, Sakellaridis and Venkatesh. In this article, we review the definition and properties of S-dual. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06303 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | S-dual of Hamiltonian $\mathbf G$ spaces and relative Langlands duality Nakajima, Hiraku Algebraic Geometry High Energy Physics - Theory Mathematical Physics Differential Geometry Representation Theory The S-dual $(\mathbf G^\vee\curvearrowright\mathbf M^\vee)$ of the pair $(\mathbf G\curvearrowright\mathbf M)$ of a smooth affine algebraic symplectic manifold $\mathbf M$ with hamiltonian action of a complex reductive group $\mathbf G$ was introduced implicitly in [arXiv:1706.02112] and explicitly in [arXiv:1807.09038] under the cotangent type assumption. The definition was a modification of the definition of Coulomb branches of gauge theories in [arXiv:1601.03586]. It was motivated by the S-duality of boundary conditions of 4-dimensional $\mathcal N=4$ super Yang-Mills theory, studied by Gaiotto and Witten [arXiv:0807.3720]. It is also relevant to the relative Langlands duality proposed by Ben-Zvi, Sakellaridis and Venkatesh. In this article, we review the definition and properties of S-dual. |
| title | S-dual of Hamiltonian $\mathbf G$ spaces and relative Langlands duality |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2409.06303 |