发表机构
Sorbonne Université; CNRS; University of Wisconsin–Madison（索邦大学; 法国国家科学研究中心; 威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文提出基于大语言模型的智能体框架Solver Agent，用于数学和理论物理计算，并应用于F-理论中O3-平面和S-折叠的提升，建立了Calabi-Yau四维流形的充分条件，并推导了D3-膜电荷修正。
AI 中文摘要
我们引入了求解器智能体（Solver Agent），这是一个基于大型语言模型的AI框架，用于数学和理论物理中的计算与证明。求解过程通过一个持久化账本进行跟踪，该账本记录假设、推导和计算。一个中心智能体将任务委派给专门的子智能体，而独立的智能体则验证中间步骤和最终结果。这种设置提高了计算机辅助计算的可追溯性、可复现性和可验证性。应用求解器智能体，我们研究了Type IIB定向折叠及其S-折叠推广的全局F-理论提升。我们为具有终端Z_k商奇点（k∈{2,3,4,6}）的射影三维流形上的Weierstrass模型建立了充分条件，使其给出具有孤立Gorenstein终端商奇点的Q-因子射影椭圆纤维Calabi-Yau四维流形。这些几何实现了O3-平面和S-折叠，其中后者的局部D3-膜探针产生四维N=3超共形场论。利用弦论不变量，我们推导了Hodge数据和欧拉特征数的定点贡献，并表明这些欧拉修正决定了实现蝌蚪消除所需的局域D3-膜电荷。我们使用环面超曲面构造来说明这些结果，其中单个三维多胞形同时确定Type IIB Calabi-Yau三维流形和F-理论基；在这里，定向折叠双覆盖自然形成具有离散Z_2规范对称性的替代属一纤维提升的二等分。最后，我们提供了在具有非阿贝尔规范扇区的四维N=1紧化中进行环面计算和四形式通量分析的方法。
英文摘要
We introduce Solver Agent, an AI framework based on large language models for calculations and proofs in mathematics and theoretical physics. The solution process is tracked through a persistent ledger that records assumptions, derivations, and computations. A central agent delegates tasks to specialized sub-agents, while independent agents verify both intermediate steps and the final result. This setup improves the traceability, reproducibility, and verification of computer-assisted calculations. Applying Solver Agent, we study global F-theory uplifts of Type IIB orientifolds and their S-fold generalizations. We establish sufficient conditions for Weierstrass models over projective threefolds with terminal $\mathbb{Z}_k$ quotient singularities ($k\in\{2,3,4,6\}$) to give $\mathbb{Q}$-factorial projective elliptically fibered Calabi-Yau fourfolds with isolated Gorenstein terminal quotient singularities. These geometries realize O3-planes and S-folds, where local D3-brane probes of the latter yield four-dimensional $\mathcal{N}=3$ superconformal field theories. Using stringy invariants, we derive fixed-point contributions to Hodge data and Euler characteristics, and show that these Euler corrections determine the localized D3-brane charges required for tadpole cancellation. We illustrate these results using toric hypersurface constructions, where a single three-dimensional polytope determines both the Type IIB Calabi-Yau threefold and the F-theory base; here, the orientifold double cover naturally forms a bisection of an alternative genus-one-fibered uplift with discrete $\mathbb{Z}_2$ gauge symmetry. Finally, we provide methods for toric computations and four-form flux analysis in four-dimensional $\mathcal{N}=1$ compactifications with non-abelian gauge sectors.
CommentsComments: 85 pages + appendices. Solver Agent is available in https://github.com/starrfree/solver-agent. Sessions for reproducibility are available in https://storage.googleapis.com/solver-agent-sessions/solver-agent-f-theory-uplifts/index.html. Further codes in https://github.com/alexmininno/orientifold_databases
