AI 中文总结
本文利用阿普利类构造三维赫尔 - 斯特罗明格系统的解族，壳外沿阿普利类变形共形平衡度量，壳上用相关厄米特\((1,1)\)形式调整满足反常消除条件，经隐函数定理得解族，改进先前工作并可扩展到\(n\)维。
AI 中文摘要
在本文中，我们使用阿普利类构造了一族三维赫尔 - 斯特罗明格系统的解，而无需在切丛上引入辅助规范联络。具体而言，我们在壳外沿着阿普利类使共形平衡度量变形，然后在壳上通过依赖于该阿普利类的厄米特\((1,1)\)形式对其进行调整以满足反常消除条件。然后通过隐函数定理得到解族的存在性。这改进了先前的工作，因为无需引入辅助规范联络，从而使期望维度与博特 - 切尔恩参数相匹配。这种阿普利参数的构造也扩展到了\(n\)维赫尔 - 斯特罗明格系统。
英文摘要
In this paper, we construct a family of solutions to the $3$-fold Hull-Strominger system using the Aeppli class, without introducing the auxiliary gauge connection on the tangent bundle. In particular, we deform the conformally balanced metric along an Aeppli class off-shell and then tune it by a hermitian $(1,1)$-form dependent on this Aeppli class on-shell to satisfy the anomaly cancellation condition. The existence of the family of solutions is then obtained by the implicit function theorem. This refines the previous work by not introducing auxiliary gauge connection, thereby matching the expected dimension with the Bott-Chern parameter. This construction of the Aeppli parameter also extends to the $n$-fold Hull-Strominger system.
Comments21 pages, 3 appendices
