Symmetries of Everything

Details Symmetries of Everything Symmetries of Everything

2001-03-12

arxiv.org/abs/math-ph/0103013v3

Physics

Mathematical Physics

Some notes added and flawed definition of mb(3|8) corrected once again. This became acute after the appearance of a recent pap

Scientific paper

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: 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. 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 of fermions, absense of proton decay, no additional gauge bosons, manifest CP violation, and particle/anti-particle asymmetry. I discuss classifications supporting the claim that every conceivable symmetry is known.

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