Constraining Conformal Correlators

Résumé fourni par la source

This page contains supplementary files to the paper Constraining Conformal Correlators by Viktoriia Borovik, Claire de Korte, Nathan Meurrens, and Dmitrii Pavlov. The files are organised in three .zip archives: PolytopesAndRelations.zip, MathematicaNotebooks.zip and Datasets.zip. We now describe the contents of each archive. The archive PolytopesAndRelations.zip contains the following files: PHVrelations.m2: this is a Macaulay2 file. It is used to compute the Hilbert function of the polynomial ring $\mathbb{C}[H_{ij},\mathcal{V}_{ij}]$ in Section 6 of the paper. This is done numerically by evaluating all monomials of given degree at many random points, recording the values into a matrix and computing its rank. Example 3-11.pdf: This file contains the expressions for Ehrhart polynomials appearing in Example 3.11. Example 3-14.txt contains the expression for the quasipolynomial from Example 3.14. conformal_polytopes.jl: This is a Julia module generating input data for the barvinok package used in Section 3.2. Instructions on how to run it are contained in the file. The folder barv contains the input files for barvinok. The folder isl contains the output files of barvinok. The archive MathematicaNotebooks.zip contains the following files. The file Differential Operators in Embedding space.nb rewrites the operators $\mathcal{D}_{1,1}$ and $\mathcal{D}_{1,2}$ from Section 8 in terms of basic building blocks. It is accompanied by the auxiliary files FinalSolutionD2WithA2.m and SimplifiedD2Action.m that should be placed in the same directory as the notebook. The results of this rewriting procedure are stored in the files D1Solution.m and D2Solution.m. The file DifferentialOperator D12.nb further processes the output for the operator $\mathcal{D}_{1,2}$. Finally, the file Constraining Conformal Three-Point Functions.nb contains the code generating three-point structures in embedding space with given spins and scaling dimensions, subject to Bose symmetry and partial conservation. To run it, the files D1Solution.m and D2Solution.m are necessary. The archive Datasets.zip contains four .csv files with counts of independent (over $\mathbb{C}$) monomials in the variables $H_{ij}$ and $\mathcal{V}_{ij}$ of given multidegree. The files 3pointmonomials.csv, 4pointmonomials.csv, and 5pointmonomials.csv treat the case $d=3$ and $n=3,4,5$ respectively. The file 4point4dmonomials.csv treats the case $n=d=4$. The output is produced by using PHVrelations.m2.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.