标题： 拓扑弦和Higgsing树 显示英文标题

标题： Topological strings and Higgsing trees

摘要： 六维超共形场论是奇特而迷人的。 它们源于F理论在卡拉比-丘椭圆纤维化上的紧化，这使它们拥有了与弦理论和M理论各种表述之间的丰富对偶性。 在本论文中，我们考虑了扩展的椭圆纤维化族，这些纤维化导致通过希格斯转变连接的六维理论。 这些族不仅涵盖了特定流形的模空间，还包括具有不同拓扑结构的其他流形。 我们的研究从两个不同的角度关注秩1的六维超共形场论。 在第四章中，我们利用来自全纯异常方程的模性，以雅可比模形式的形式计算拓扑弦的分划函数。 我们还提供了一个从其父理论获得希格斯理论的拓扑分划函数的方案。 通过这种方法，我们可以解释在我们的研究中观察到的许多对称性增强现象。 另一方面，在第五章中，我们探讨了六维理论的二维孤子，即非临界弦。 这种非临界弦的椭圆亏格与拓扑弦分划函数的一部分相吻合。 通过仔细研究这种非临界弦，我们提出了一个关于椭圆亏格的假设，该假设用相关电流代数的特征标来表达。 我们提供了支持该假设有效性的有力证据，并揭示了这些非临界弦的椭圆亏格的新封闭形式表达式。 通过这些研究，我们希望揭示六维超共形场论的迷人世界，并深入了解它们卓越的特性和联系。 显示英文摘要

摘要： 6-dimensional superconformal field theories are exotic and fascinating. They emerge from compactifications of F-theory on Calabi-Yau elliptic fibrations, which grants them a rich array of dualities with various other formulations of string and M-theory. In this thesis, we consider extended families of elliptic fibrations, giving rise to 6d theories connected by Higgs transitions. These families not only encompass the moduli space of a specific manifold but also include other manifolds with different topologies. Our investigation focuses on rank 1 6D superconformal field theories from two distinct angles. In Chapter 4, we employ modularity, which arises from the holomorphic anomaly equations, to compute the topological string partition function in terms of Jacobi modular forms. We also provide a prescription for obtaining the topological partition function of a Higgsed theory from its parent. Through this approach, we can explain numerous symmetry enhancements that we observed in our study. On the other hand, in Chapter 5, we explore the 2D soliton of the 6D theory, the non-critical string. The elliptic genus of this non-critical string coincides with a part of the topological string partition function. By carefully studying this non-critical string, we propose an ansatz for the elliptic genera expressed in terms of characters of the associated current algebras. We present compelling evidence supporting the validity of this ansatz and unveil novel closed form expressions for the elliptic genera of these non-critical strings. Through these investigations, we hope to shed light on the intriguing world of 6D superconformal field theories and uncover new insights into their remarkable properties and connections.