发表机构
Indian Institute of Technology, Gandhinagar（印度理工学院甘地纳加尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过计算亏格一谱曲线的平移和旋转矩阵，重构了超对称LG理论的世界面关联函数，建立了双割矩阵模型与更高亏格几何之间的显式对偶词典。
AI 中文摘要
我们计算了与亏格一谱曲线相关联的高阶平移（$\mathcal{T}$）和旋转（$\mathcal{R}$）矩阵。利用这些数据，我们重构了相应的超对称Landau--Ginzburg（LG）理论中顶点算子的世界面关联函数。这提供了从亏格零、单割谱曲线构造到更高亏格几何的推广。矩阵模型关联函数被映射到对称六次双阱势的黎曼曲面模空间上的积分，该势具有双割解。我们进一步识别了世界面积分顶点算子中的有理部分和椭圆部分，并表明每个部分都精确对应于矩阵模型中单迹算子的相应关联函数。总的来说，我们的构造展示了更高亏格谱曲线数据、相关的上同调场论（CohFT）以及相应矩阵模型可观测量世界面描述之间的显式词典。
英文摘要
We compute the higher-rank translation ($\mathcal{T}$) and rotation ($\mathcal{R}$) matrices associated with a genus-one spectral curve. Using these data, we reconstruct the worldsheet correlators of vertex operators in the corresponding supersymmetric Landau--Ginzburg (LG) theory. This provides a generalization of the genus-zero, one-cut spectral-curve construction to higher-genus geometries. The matrix-model correlators are mapped to integrals over the moduli space of Riemann surfaces for the symmetric sextic double-well potential, which has a double-cut solution. We further identify the rational and elliptic contributions to the worldsheet integrated vertex operators and show that each of the sector precisely matches the corresponding correlators of single-trace operators in the matrix model. Altogether, our construction showcases an explicit dictionary between the higher-genus spectral-curve data, the associated Cohomological field theory (CohFT), and the worldsheet description of the corresponding matrix-model observables.
Comments71 pages, 8 figures. Comments are welcome!
