论文标题
$ \ widehat {z} $在大$ n $：从曲线计数到量子模块化
$\widehat{Z}$ at large $N$: from curve counts to quantum modularity
论文作者
论文摘要
在3个manifold $ y $上降低6D五脑理论，提供了$ q $ series 3-manifold variant $ \ widehat {z}（y）$。我们分析了$ f_k = \ widehat {z}（m_k）$的大$ n $行为，其中$ m_k $是3速phere中一个结$ k $的补充，并探索$ a $ a $ a $ a-a $ a-a $ a $ a = q^n $）版本的$ f_ {k} $ f_ {k} $ {k} $ {k} $和homefly-pt polynomials。一方面，结合了结的圆周格anuli的数量，这对$ f_k $在开放式全体形态曲线方面提供了枚举的解释。另一方面，它导致$ a $ a $ a的$ f_k $ for $（2,2p+1）$ - torus结的封闭式表达式。他们建议进一步基于超级单位的$ t $变信息，可用于获得ADO多项式的$ t $变形，预计将与分类有关。此外，研究$ f_k $在$ k $上的自然几何操作下如何变换表明在新环境中与量子模块化的关系。
Reducing a 6d fivebrane theory on a 3-manifold $Y$ gives a $q$-series 3-manifold invariant $\widehat{Z}(Y)$. We analyse the large-$N$ behaviour of $F_K=\widehat{Z}(M_K)$, where $M_K$ is the complement of a knot $K$ in the 3-sphere, and explore the relationship between an $a$-deformed ($a=q^N$) version of $F_{K}$ and HOMFLY-PT polynomials. On the one hand, in combination with counts of holomorphic annuli on knot complements, this gives an enumerative interpretation of $F_K$ in terms of counts of open holomorphic curves. On the other, it leads to closed form expressions for $a$-deformed $F_K$ for $(2,2p+1)$-torus knots. They suggest a further $t$-deformation based on superpolynomials, which can be used to obtain a $t$-deformation of ADO polynomials, expected to be related to categorification. Moreover, studying how $F_K$ transforms under natural geometric operations on $K$ indicates relations to quantum modularity in a new setting.
