AI 中文总结
CasimirRFM是一款Mathematica软件包，可实现黎曼平坦流形紧化的卡西米尔能量计算，支持多种场论与超引力场景，通过IIB型超引力紧化示例验证其功能。
AI 中文摘要
CasimirRFM是一款用于研究黎曼平坦流形紧化以及计算高维场论和超引力中一圈卡西米尔能量的Mathematica软件包。它采用Ewald求和实现晶格和的高效数值计算，可计算低维卡西米尔势和局域高维卡西米尔能量密度，支持一般无质量谱和扭曲边界条件。该软件包提供工具构建和分析定义这些流形的有限群，确定不变度量和上同调基，识别兼容的自旋结构，计算模空间度量；还可计算引力子、p-形式、旋量和Rarita-Schwinger表示中的和乐元迹。我们描述该软件包的数学表述与数值实现，并通过IIB型超引力在T⁶/ℤ₈上的紧化示例说明其使用，包括卡西米尔势计算和局域化卡西米尔-膜贡献的可视化。
英文摘要
CasimirRFM is a Mathematica package for the study of compactifications on Riemann-flat manifolds and the computation of one-loop Casimir energies in higher-dimensional field theories and supergravity. It implements an efficient numerical evaluation of lattice sums using Ewald summation, and computes both lower-dimensional Casimir potentials and local higher-dimensional Casimir energy densities, allowing for general massless spectra and twisted boundary conditions. The package provides tools for constructing and analysing the finite groups defining these manifolds, determining invariant metrics and cohomology bases, identifying compatible spin structures, and computing moduli-space metrics. Moreover, it evaluates the traces of holonomy elements in the graviton, $p$-form, spinor, and Rarita-Schwinger representations. We describe the mathematical formulation and numerical implementation of the package, and illustrate its use through a compactification of Type IIB supergravity on $T^6/\mathbb{Z}_8$, including the computation of the Casimir potential and the visualization of localised Casimir-brane contributions.
Comments30 pages, 4 tables; GitHub link: https://github.com/bruno-valeixo-bento/CasimirRFM
