@MISC{Larsson08symmetriesof, author = {T. A. Larsson}, title = {Symmetries of Everything}, year = {2008} }

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Abstract

I argue that string theory can not be a serious candidate for the Theory of Everything, not because it lacks experimental support, but because of its algebraic shallowness. I describe two classes of algebraic structures which are deeper and more general than anything seen in string theory: 1. The multi-dimensional Virasoro algebras, i.e. the abelian but non-central extension of the algebra of vector fields in N dimensions by its module of closed dual one-forms. 2. The exceptional simple Lie superalgebra mb(3|8), which is the deepest possible symmetry (depth 3 in its consistent Weisfeiler grading). The grade zero subalgebra, which largely governs the representation theory, is the standard model algebra sl(3)⊕sl(2)⊕ gl(1). Some general features can be extracted from an mb(3|8) gauge theory even before its detailed construction: several generations