标题： 从一个单极环面得到的$K$理论的Coulomb分支的对偶性 显示英文标题

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

摘要： 我们考虑一个单孔环面的量化$\mathrm{SL}_2$-特征簇。 我们证明这个量化代数有三个$\mathbb{Z}_2$-不变子代数，这些子代数在Braverman、Finkelberg和Nakajima的意义下与量化的$K$-理论上的Coulomb分支同构。 这些子代数被$\mathrm{SL}_2(\mathbb{Z})$映射类群作用所置换。 我们的结果验证了物理文献中关于4d$\mathcal{N}=2^*$理论及其对偶性的各种预测。 显示英文摘要

摘要： 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.