CasimirRFM: A Mathematica package for Riemann-flat compactifications with Casimir energies

Abstract: 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 $T<sup>6/\mathbb{Z}_8$, including the computation of the Casimir potential and the visualization of localised Casimir-brane contributions.