FermatCY

This repository contains the Mathematica code used to generate the data on Fermat-type Calabi-Yau four-folds used in the paper "The Tadpole Conjecture in the Interior of Moduli Space" by S. Lüst and M. Wiesner (https://arxiv.org/pdf/2211.05128.pdf).

Content

• Fermat.nb: The main Mathematica notebook that contains all relevant code to reproduce the results and figures from the paper.
• cydata.txt: A database of 609 Fermat-type Calabi-Yau four-folds with $h^{3,1}=h_\text{poly}^{3,1}$ and $h^{3,1} - h_\text{inv}^{3,1} < 5000$. The data is stored in form of a Mathematica table. Each row contains the following elements: {{weights}, {generators}, {h33inv, h33noninv}, {rank of D2W, rank of D2W at LG point}, {timing information}, {memory usage}}. Here {weights} = {a1, a2, a3, a4, a5, a6} are the weights of the weighted projected space (see eq. (3.2) in the paper) and {generators} is a list of generators of the discrete group $G$. Each element of {generators} is of the form {{g1, g2, g3, g4, g5}, |g|} with the gi defining the action of the geneator on the projective coordinates as introduced in eq. (3.8) and |g| the order of the generator.

Reference

If you use this code, please cite the following paper:

"The Tadpole Conjecture in the Interior of Moduli Space," Severin Lüst and Max Wiesner, [arXiv:2211.05128 [hep-th]].