Symmetries of Everything
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: 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.
Cite
@article{arxiv.math-ph/0103013,
title = {Symmetries of Everything},
author = {T. A. Larsson},
journal= {arXiv preprint arXiv:math-ph/0103013},
year = {2007}
}
Comments
Some notes added and flawed definition of mb(3|8) corrected once again. This became acute after the appearance of a recent paper by D. Friedan