发表机构
Graduate School of Physics, University of Tokyo; Trans-Scale Quantum Science Institute, University of Tokyo（东京大学物理学研究生院; 东京大学跨尺度量子科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
推导出二维含\(\mathcal{N}\geq2\)超荷的椭圆亏格及其一维、零维对应物的新精确公式，结果表示为对晶体几何/组合结构的离散和，推广了Nekrasov配分函数并揭示新组合学。
AI 中文摘要
我们推导了具有\(\mathcal{N}\geq2\)超荷的二维时空椭圆亏格及其一维和零维对应物（对于Witten指标和矩阵模型配分函数）的新精确公式。我们的结果写成作者之前引入的晶体的几何/组合结构的离散和。每个晶体的贡献可以用称为分子的晶体有限子结构的边界数据来表示。我们的结果提供了由杨图枚举的著名Nekrasov配分函数的广泛推广，并揭示了晶体熔化背后的新组合学。我们还分析了与复曲面Calabi-Yau四维相关的二维\(\mathcal{N}=(0,2)\)理论产生的晶体的热力学极限，其中在极限中出现了Calabi-Yau几何的投影。
英文摘要
We derive new exact formulae for elliptic genera in two spacetime dimensions with $\mathcal{N}\ge 2$ supercharges, as well as their one- and zero-dimensional counterparts (for Witten indices and matrix-model partition functions). Our results are written as a discrete sum over geometric/combinatorial structures of crystals introduced previously by the authors. The contribution from each crystal may be expressed in terms of the boundary data of a finite substructure of the crystal called the molecules. Our results provide vast generalisations of the celebrated Nekrasov partition function enumerated by the Young diagrams, and uncover new combinatorics underlying the crystal melting. We also analyse the thermodynamic limit of crystals arising from two-dimensional $\mathcal{N}=(0,2)$ theories associated with toric Calabi-Yau fourfolds, where a projection of the Calabi-Yau geometry emerges in the limit.
Comments44 pages, 3 figures; v2: minor corrections and some more comments added
Journal refJHEP09(2026)244
