论文标题
Yangian不变性的渔网积分在2个维度上作为卡拉比Yau品种的体积
Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
论文作者
论文摘要
我们认为，$ \ ell $ -loop Yangian-Invariant Fishnet积分在两个维度上与Calabi-yau $ \ ell $ -folds的家族相连。积分的价值可以从卡拉比（Calabi-Yau）的周期中计算出来，而孙子发电机（Yangian Generator）提供其Picard-fuchs差异理想。使用镜像对称性，我们可以将积分不可或缺的值确定为镜面calabi-yau的量子体积。我们发现，类似于字符串理论中发生的事情，对于$ \ ell = 1 $和2，积分的值与镜像的经典音量一致，但是从$ \ ell = 3 $开始，经典卷可以通过Instanton贡献来纠正。我们在几个示例中说明了这些主张，并使用它们为2环和3循环的Yangian-Invariant Traintrack积分的首次结果提供了两个维度的内部动力学。
We argue that $\ell$-loop Yangian-invariant fishnet integrals in 2 dimensions are connected to a family of Calabi-Yau $\ell$-folds. The value of the integral can be computed from the periods of the Calabi-Yau, while the Yangian generators provide its Picard-Fuchs differential ideal. Using mirror symmetry, we can identify the value of the integral as the quantum volume of the mirror Calabi-Yau. We find that, similar to what happens in string theory, for $\ell=1$ and 2 the value of the integral agrees with the classical volume of the mirror, but starting from $\ell=3$, the classical volume gets corrected by instanton contributions. We illustrate these claims on several examples, and we use them to provide for the first time results for 2- and 3-loop Yangian-invariant traintrack integrals in 2 dimensions for arbitrary external kinematics.
