Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917604875042816 |
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| author | Borot, Gaëtan Bouchard, Vincent Chidambaram, Nitin Kumar Creutzig, Thomas |
| author_facet | Borot, Gaëtan Bouchard, Vincent Chidambaram, Nitin Kumar Creutzig, Thomas |
| contents | We identify Whittaker vectors for $\mathcal{W}_k(\mathfrak{g})$-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of $G$-bundles over $\mathbb{P}^2$ for $G$ a complex simple Lie group, can be computed by a non-commutative version of the Chekhov-Eynard-Orantin topological recursion. We formulate the connection to higher Airy structures for Gaiotto vectors of type A, B, C, and D, and explicitly construct the topological recursion for type A (at arbitrary level) and type B (at self-dual level). On the physics side, it means that the Nekrasov partition function for pure $\mathcal{N} = 2$ four-dimensional supersymmetric gauge theories can be accessed by topological recursion methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_04516 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Whittaker vectors for $\mathcal{W}$-algebras from topological recursion Borot, Gaëtan Bouchard, Vincent Chidambaram, Nitin Kumar Creutzig, Thomas Mathematical Physics High Energy Physics - Theory Representation Theory 14H81, 17B69, 81R60, 81T13, 81T40 We identify Whittaker vectors for $\mathcal{W}_k(\mathfrak{g})$-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of $G$-bundles over $\mathbb{P}^2$ for $G$ a complex simple Lie group, can be computed by a non-commutative version of the Chekhov-Eynard-Orantin topological recursion. We formulate the connection to higher Airy structures for Gaiotto vectors of type A, B, C, and D, and explicitly construct the topological recursion for type A (at arbitrary level) and type B (at self-dual level). On the physics side, it means that the Nekrasov partition function for pure $\mathcal{N} = 2$ four-dimensional supersymmetric gauge theories can be accessed by topological recursion methods. |
| title | Whittaker vectors for $\mathcal{W}$-algebras from topological recursion |
| topic | Mathematical Physics High Energy Physics - Theory Representation Theory 14H81, 17B69, 81R60, 81T13, 81T40 |
| url | https://arxiv.org/abs/2104.04516 |