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arXiv · 2411.17378

Dualities of $K$-theoretic Coulomb branches from a once-punctured torus

Dylan G. L. Allegretti·Peng Shan
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Abstract

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.

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BibTeXRIS

Dylan G. L. Allegretti, Peng Shan. 2024-11-26. Dualities of $K$-theoretic Coulomb branches from a once-punctured torus. https://arxiv.org/abs/2411.17378

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