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arXiv 2106.09807hep-th
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1-形式对称、孤立N = 2 SCFT和卡-丘三重

1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds

Matthew Buican, Hongliang Jiang

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84 pages; v2: references added, minor typos fixed, minor additional result (direct proof of corollary 1)
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摘要：

我们系统地研究了四维$\mathcal{N}=2$超共形场论，这些场论可以通过IIB型弦论在嵌入$\mathbb{C}^4$的孤立超曲面奇点上构造。我们表明，如果在这个类的理论没有$\mathcal{N}=2$-保持精确的边缘变形（即，该理论被孤立为一个$\mathcal{N}=2$ SCFT），则它没有1-形式对称性。这种情况有点让人想起二维量子场论中的1-形式对称和分解。此外，我们的研究结果表明，从IHS产生的理论，1-形式的对称性起源于规范群（与消失的β函数）。我们的讨论的一个推论是，有没有1-形式的对称性IHS理论，所有的库仑支手征环生成标度维小于2。根据$a$和$c$中心电荷，这个条件意味着满足$a<{1\over24}(15r+2f)$和$c<{1\over6}(3r+f)$（其中$r$是库仑分支的复维数，$f$是连续0-形式味对称的秩）的IHS理论没有1-形式对称性。在回顾了其他理论的1-型对称性之后，我们推测一般的相互作用四维$\mathcal{N}=2$ SCFT的库仑支手征环生成元的维数小于2时不具有1-型对称性.

英文摘要：

We systematically study 4D $\mathcal{N}=2$ superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in $\mathbb{C}^4$. We show that if a theory in this class has no $\mathcal{N}=2$-preserving exactly marginal deformation (i.e., the theory is isolated as an $\mathcal{N}=2$ SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the $a$ and $c$ central charges, this condition implies that IHS theories satisfying $a<{1\over24}(15r+2f)$ and $c<{1\over6}(3r+f)$ (where $r$ is the complex dimension of the Coulomb branch, and $f$ is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D $\mathcal{N}=2$ SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

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