论文标题
迈向2D理性SCFT的理论特征
Towards Hodge Theoretic Characterizations of 2d Rational SCFTs
论文作者
论文摘要
对模量空间中有理顺式田间理论的研究特别令人感兴趣，因为这些理论对应于模量空间中的点和算术结构通常更丰富，同时也是发生非琐事物理学的点（例如，在吸引人的黑洞和BPS状态的研究中，在合理点的研究中）。这导致了对这种理性观点进行表征和分类的各种尝试。在本文中，仔细分析了有理共同场理论的Gukov-vafa的猜想，其目标空间是Ricci FlatKähler歧管，以仔细分析了环形紧凑型的情况。我们使用$ t^4 $压缩作为测试案例来完善猜想的说法，并努力验证它。关于霍迪格理论（包括复杂乘法）的七个共同属性已被确定，以$ t^4 $ -target有理保形理论。但是，通过将七个属性施加到七个属性中，仍然存在$ \ MATHCAL n =（1,1）$ scfts，这些属性不是理性的。讨论了开放的问题，含义和未来的工作路线。
The study of rational conformal field theories in the moduli space is of particular interest since these theories correspond to points in moduli space where the algebraic and arithmetic structure are usually richer, while also being points where non--trivial physics occurs (such as in the study of attractor black holes and BPS states at rational points). This has led to various attempts to characterize and classify such rational points. In this paper, a conjectured characterization by Gukov--Vafa of rational conformal field theories whose target space is a Ricci flat Kähler manifold is analyzed carefully for the case of toroidal compactifications. We refine the conjectured statement as well as making an effort to verify it, using $T^4$ compactification as a test case. Seven common properties in terms of Hodge theory (including complex multiplication) have been identified for $T^4$-target rational conformal field theories. By imposing three properties out of the seven, however, there remain $\mathcal N = (1,1)$ SCFTs that are not rational. Open questions, implications and future lines of work are discussed.
