发表机构
Google DeepMind; Institut de Physique Théorique, Université Paris Saclay, CNRS, CEA; Laboratoire d’Annecy-le-Vieux de Physique Théorique (LAPTh), CNRS and Université Savoie Mont-Blanc（谷歌DeepMind; 巴黎萨克雷大学理论物理研究所; 阿讷西勒沃旧理论物理实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了等质量二维(n-1)圈日落费曼积分与局部Calabi-Yau n-fold的亏格0一点后代不变量的精确恒等式，还得到镜像映射的单叶性等结果，为相关理论提供了关键联系与约束。
AI 中文摘要
我们证明了一个精确恒等式：对于n≥4，等质量二维(n-1)圈日落费曼积分，与局部Calabi-Yau n-fold Xₙ=Tot(K_{Fₙ})的亏格0一点后代不变量，在大欧几里得动量处作为收敛对数芽相等，其中Fₙ⊂(ℙ¹)ⁿ是光滑的(1,…,1)超曲面。记s为动量变量，y=-1/s，该恒等式为I^{(n-1)}_{\u229d}(s)=(-1)^{n-1}yA[nR^{n-1}-θ_Q𝒟₀^Δ R^{n-2}+∑_{j=0}^{n-3}c_jR^j]，其中R=log y+O(y)是局部镜像坐标，A=θ_yR，Q=e^R，𝒟₀^Δ(Q)是主一点势，每个c_j是1、后代级数𝒟_a^Δ(Q)及其导数θ_Q𝒟_a^Δ（0≤a≤n-2）的显式线性组合，系数来自Gamma类的奇zeta值ℚ[ζ(3),ζ(5),…]。后代级数由环境超几何级数和逆镜像映射显式给出。我们还证明了主镜像映射的全局单叶性，给出Q-Taylor半径的显式上下界，提取完整主赋值除子及其积分覆盖变换，并将环境端点常数约化为有限通用Gamma类部分和⌊(n-1)/2⌋个实参数。
英文摘要
We prove an exact identity, as convergent logarithmic germs at large Euclidean momentum, between the equal-mass two-dimensional $(n-1)$-loop sunset Feynman integral, with $n\geq4$, and the genus-zero one-point descendant invariants of the local Calabi--Yau $n$-fold $X_n=\operatorname{Tot}(K_{F_n})$, where $F_n\subset(\mathbb P^1)^{n}$ is a smooth $(1,\ldots,1)$ hypersurface. Writing $s$ for the momentum variable and $y=-1/s$, the identity reads $$ I^{(n-1)}_{\circleddash}(s)=(-1)^{n-1}yA\,\Bigl[nR^{n-1}-θ_Q{\mathcal D}_0^Δ\,R^{n-2} +\sum_{j=0}^{n-3}c_jR^j\Bigr], $$ where $R=\log y+O(y)$ is the local mirror coordinate, $A=θ_yR$, $Q=e^R$, ${\mathcal D}_0^Δ(Q)$ is the primary one-point potential, and each $c_j$ is an explicit linear combination of $1$, the descendant series ${\mathcal D}_a^Δ(Q)$ and their derivatives $θ_Q{\mathcal D}_a^Δ$, $0\leq a\leq n-2$, with coefficients in the odd-zeta values $\mathbb Q[ζ(3),ζ(5),\ldots]$ coming from the Gamma class. The descendant series are given explicitly by the ambient hypergeometric series and the inverse mirror map. We also prove global univalence of the principal mirror map, with explicit upper and lower bounds on the $Q$-Taylor radii, extract the full primary evaluation divisor and its integral cover transform, and reduce the ambient endpoint constants to a finite universal Gamma-class part and $\lfloor(n-1)/2\rfloor$ real parameters.
Comments88 pages. Implementation codes available at https://github.com/pierrevanhove/Sunset-Gromov-Witten
