论文标题
3D镜像对称和量子$ k $ - 高渗品种的理论
3d Mirror Symmetry and Quantum $K$-theory of Hypertoric Varieties
论文作者
论文摘要
遵循Aganagic-okounkov \ cite {aoelliptic}的想法，我们研究了高信品种的顶点函数，由$ k $ - 从$ \ mathbb {p}^1 $中定义的准理论计数。我们证明了3D镜像对称性陈述，即3D高音镜对的两组$ q $ - 差异方程相互等效，而Kähler和Equivariant参数交换了，并且是相反的偏振化选择。 3D镜对的顶点函数，作为$ Q $差异方程的解决方案，满足特定的渐近条件，与椭圆稳定信封有关。还讨论了各种量子$ k $的概念 - 高渗品种的理论。
Following the idea of Aganagic--Okounkov \cite{AOelliptic}, we study vertex functions for hypertoric varieties, defined by $K$-theoretic counting of quasimaps from $\mathbb{P}^1$. We prove the 3d mirror symmetry statement that the two sets of $q$-difference equations of a 3d hypertoric mirror pairs are equivalent to each other, with Kähler and equivariant parameters exchanged, and the opposite choice of polarization. Vertex functions of a 3d mirror pair, as solutions to the $q$-difference equations, satisfying particular asymptotic conditions, are related by the elliptic stable envelopes. Various notions of quantum $K$-theory for hypertoric varieties are also discussed.
