环面上的超刘维尔理论：自举与超 Virasoro 极小弦
Super Liouville theory on the torus: bootstrap and the super Virasoro minimal string
浏览论文内容
中文总结 AI 辅助
本文研究环面上的超刘维尔理论，纠正了超 Virasoro 块并构造模穿越核，进而分析超 Virasoro 极小弦，验证其振幅与拓扑递归一致，并识别出特殊 Ramond 插入。
中文摘要 AI 辅助
受低维世界sheet弦构造应用的启发，我们分析了环面上的 $\mathcal{N}=1$ 超刘维尔理论。具体而言，我们重新审视了文献中构造的环面一点超 Virasoro 块的递归表示，并纠正了其中的若干要素。在此过程中，我们在奇自旋结构中识别出一个新的块，它与一个特殊的超后裔相关联，其环面一点函数变换方式类似于 Virasoro 初级场。随后，我们证明了类空和类时超刘维尔理论的结构常数均满足模穿越。此外，我们利用自举论证为所有四个自旋结构扇区构造了模穿越核，这些核适用于中心荷 $c \in \mathbb{C}\setminus(-\infty,\tfrac{3}{2}]$，并验证了它们正确实现了块的穿越变换。作为该技术的具体应用，我们分析了超 Virasoro 极小弦。共有四种这样的理论，$\mathrm{0A}^{\pm}$ 和 $\mathrm{0B}^{\pm}$，它们通过 GSO 投影以及世界sheet超荷的选择来区分。结果表明，所得的 NS 扇区球面三点和环面一点振幅与对偶矩阵积分谱曲线上的拓扑递归一致，而这些谱曲线最近由三维超引力推导得出。值得注意的是，特殊超后裔的一点函数在对奇自旋结构对环面振幅的贡献中起着至关重要的作用，这通过对图像改变算子的仔细处理得以实现。我们还识别出 $\mathrm{0A}^{-}$ 理论中一个特殊的零动量 Ramond 插入，我们将其几何上解释为 Ramond 穿刺，并将其混合球面三点振幅与相应的相交理论预测相匹配。
英文摘要
Motivated by applications to low-dimensional worldsheet string constructions, we analyze $\mathcal{N} = 1$ super Liouville theory on the torus. Specifically, we re-examine the recursive representations of the torus one-point super Virasoro blocks that have been constructed in the literature and correct several of their ingredients. In the process we identify a new block in the odd spin structure, associated with a privileged superdescendant whose torus one-point function transforms like that of a Virasoro primary. We then demonstrate that the structure constants for both spacelike and timelike super Liouville theory satisfy modular crossing. Furthermore, we use a bootstrap argument to construct modular crossing kernels for all four spin structure sectors, valid for central charges $c \in \mathbb{C}\setminus(-\infty,\tfrac{3}{2}]$, and verify that they correctly implement the crossing transformations of the blocks. As a concrete application of the technology, we analyze the super Virasoro minimal string. There are four such theories, $\mathrm{0A}^{\pm}$ and $\mathrm{0B}^{\pm}$, which are distinguished by the GSO projection together with the choice of worldsheet supercharge. The resulting NS-sector sphere three-point and torus one-point amplitudes are shown to agree with topological recursion on the spectral curves of the dual matrix integrals, which were recently derived from 3d supergravity. Notably, the one-point function of the privileged superdescendant plays an essential role in the contribution of the odd spin structure to the torus amplitude via a careful treatment of the picture changing operator. We also identify an exceptional zero-momentum Ramond insertion in the $\mathrm{0A}^{-}$ theory that we interpret geometrically as a Ramond puncture, and match its mixed sphere three-point amplitude to the corresponding intersection theory prediction.
发表机构
- Syracuse University（雪城大学）
- Institute for Advanced Study（高等研究院）
- University of California, Davis（加州大学戴维斯分校）
- École Normale Supérieure（巴黎高等师范学院）
- Université PSL（巴黎文理研究大学）
- CNRS（法国国家科学研究中心）
- Sorbonne Université（索邦大学）
- Université Paris Cité（巴黎西岱大学）
机构由 AI 辅助整理，请以论文原文为准。
