三维中的镜像对称
Mirror symmetry in 3d in 3d mirror symmetry
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中文总结 AI 辅助
研究紧致CY3流形\(Y\)相关的\(X\)和\(X^{!}\)的三维镜像对称现象，通过三维SYZ构造、DT理论等方法，展现了它们之间包括膜构造及角色互换等的对称关系。
中文摘要 AI 辅助
给定一个紧致CY3流形\(Y\)，其A侧（相应地，B侧）的通用中间雅可比\(X\)（相应地，\(X^{!}\)）具有自然的超凯勒结构。\(X\)和\(X^{!}\)在A模型和B模型中都确定了三维Rozansky-Witten理论。描述了\(X\)和\(X^{!}\)之间一些惊人的三维镜像对称现象。包括从\(X\)通过\(X\)中某些三维A膜的模构造\(X^{!}\)的三维SYZ构造，以及\(X^{!}\)上的三维B膜是\(X\)中余切纤维三维A膜的三维SYZ变换。在\(Y\)和\(Y^{\vee}\)的镜像对称下，\(X\)和\(X^{!}\)的角色互换。还通过DT理论以及\(Y\)和\(Y^{\vee}\)上的离散对称性在\(X\)和\(X^{!}\)中构造了三维A膜和B膜。
英文摘要
Given a compact CY3 $Y$, its A-side (resp. B-side) universal intermediate Jacobian $X$ (resp. $X^{!}$) admits a natural hyperkahler structure. Both $X$ and $X^{!}$ determines 3d Rozansky-Witten theories, in both A-model and B-model. We describe some surprising 3d mirror symmetry phenomena between $X$ and $X^{!}$. This includes (i) a 3d SYZ construction of $X^{!}$ from $X$ via moduli of certain 3d A-branes in $X$ constructed from $D^{b}\left( Y,Ω\right) $ with varying stability conditions given by $\varpi $; (ii) The 3d B-brane on $X^{!}$, constructed from varying $D^{b}\left( Y,Ω\right) $ with fixed $\varpi $, is realized as the 3d SYZ transformation of a cotangent fiber 3d A-brane in $X$. Under mirror symmetry between $Y$ and $Y^{\vee }$, the roles for $X$ and $% X^{!}$ got interchanged. We also construct 3d A- and B-branes in $X$ and $X^{!}$ via DT theory and discrete symmetries on $Y$ and $Y^{\vee }$.
