Dualities of $K$-theoretic Coulomb branches from a once-punctured torus
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Allegretti, Dylan G. L. Shan, Peng |
| author_facet | Allegretti, Dylan G. L. Shan, Peng |
| contents | We consider the quantized $\mathrm{SL}_2$-character variety of a once-punctured torus. We show that this quantized algebra has three $\mathbb{Z}_2$-invariant subalgebras that are isomorphic to quantized $K$-theoretic Coulomb branches in the sense of Braverman, Finkelberg, and Nakajima. These subalgebras are permuted by the $\mathrm{SL}_2(\mathbb{Z})$ mapping class group action. Our results confirm various predictions from the physics literature about 4d $\mathcal{N}=2^*$ theories and their dualities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dualities of $K$-theoretic Coulomb branches from a once-punctured torus Allegretti, Dylan G. L. Shan, Peng Representation Theory High Energy Physics - Theory Geometric Topology Quantum Algebra We consider the quantized $\mathrm{SL}_2$-character variety of a once-punctured torus. We show that this quantized algebra has three $\mathbb{Z}_2$-invariant subalgebras that are isomorphic to quantized $K$-theoretic Coulomb branches in the sense of Braverman, Finkelberg, and Nakajima. These subalgebras are permuted by the $\mathrm{SL}_2(\mathbb{Z})$ mapping class group action. Our results confirm various predictions from the physics literature about 4d $\mathcal{N}=2^*$ theories and their dualities. |
| title | Dualities of $K$-theoretic Coulomb branches from a once-punctured torus |
| topic | Representation Theory High Energy Physics - Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2411.17378 |