标题： Vafa-Witten 分区函数的模性来自 SymTFT 显示英文标题

标题： Modularity of Vafa-Witten Partition Functions from SymTFT

摘要： 六维 (2,0) 理论的$N$膜在乘积几何$T^2\times S$上紧致化，其中$S$是一个凯勒四维流形，可以在两种不同的极限下进行研究。在一种极限下，$T^2$的尺寸被取为零，并结合拓扑扭变，得到在$S$上的瓦法-威滕划分函数。另一方面，将$S$的尺寸取为零会导致二维$\mathcal{N}=(0,4)$理论。这产生了一个二维和四维的对应关系，其中瓦法-威滕划分函数与二维理论的特征相联系。在本文中，我们通过采用 SymTFT 技术来测试这一猜想，以证明两边的模变换性质相匹配。此外，我们构建了模不变的二维绝对划分函数，并验证它们在耦合空间中的自对偶点上对离散对称性的规范不变。这进一步表明二维 SCFT 中存在对偶缺陷。 显示英文摘要

摘要： The 6d (2,0) theory of $N$ M5 branes compactified on the product geometry $T^2\times S$, where $S$ is a K\"ahler 4-manifold, can be studied in two different limits. In one limit, the size of $T^2$ is taken to zero and together with a topological twist one arrives at the Vafa-Witten partition function on $S$. On the other hand, taking the size of $S$ to zero leads to a 2d $\mathcal{N}=(0,4)$ theory. This gives rise to a 2d-4d correspondence where the Vafa-Witten partition functions are identified with the characters of the 2d theory. In this paper, we test this conjecture for Hirzebruch and Del Pezzo surfaces by employing the technique of SymTFT to show that the modular transformation properties of the two sides match. Moreover, we construct modular invariant 2d absolute partition functions and verify that they are invariant under gauging of a discrete symmetry at the self-dual point in coupling space. This provides further hints for the presence of duality defects in the 2d SCFT.