Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories, II
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866910302997577728 |
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| author | Braverman, Alexander Finkelberg, Michael Nakajima, Hiraku |
| author_facet | Braverman, Alexander Finkelberg, Michael Nakajima, Hiraku |
| contents | Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold with an $\mathrm{SU}(2)$-action, possibly with singularities. We give a mathematical definition of the Coulomb branch as an affine algebraic variety with $\mathbb C^\times$-action when $\mathbf M$ is of a form $\mathbf N\oplus\mathbf N^*$, as the second step of the proposal given in arXiv:1503.03676. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1601_03586 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories, II Braverman, Alexander Finkelberg, Michael Nakajima, Hiraku Representation Theory High Energy Physics - Theory Mathematical Physics Algebraic Geometry Differential Geometry Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold with an $\mathrm{SU}(2)$-action, possibly with singularities. We give a mathematical definition of the Coulomb branch as an affine algebraic variety with $\mathbb C^\times$-action when $\mathbf M$ is of a form $\mathbf N\oplus\mathbf N^*$, as the second step of the proposal given in arXiv:1503.03676. |
| title | Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories, II |
| topic | Representation Theory High Energy Physics - Theory Mathematical Physics Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/1601.03586 |