New interpretation of Kaluza-Klein compactification

Abstract Utilizing Jordan algebras and superalgebras, we focus on the significant role of lattices associated with discrete subgroups of the non-compact groups of the magic square. These lattices are not just a part of the process, but they play a profound role in reformulating conformal field theories and forming superstring theories, thereby pointing to a more comprehensive theory connected with a chiral 27-dimensional lattice, which is an extension of Conway’s lattice. We also highlight our newly discovered 16-dimensional algebra, which resembles Hurwitz’s algebras and its connection to superstrings, octonionic color algebras, and Galois Fields.