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Résumé |
Using numerical bootstrap methods, we constrain the spectrum of the Laplacian operator in $d$-dimensional flat manifolds, as well as the triple integrals of its eigenmodes. We provide many examples of $d$-dimensional flat tori that populate these bounds. In certain dimensions, our bounds are saturated by some special lattices, including the $E_8$ lattice in 8d and the Leech lattice in 24d. These bounds admit an interpretation in the context of Kaluza-Klein theories and have connections with the sphere packing and kissing number problems. |
