An Exceptionally Simple Theory of Everything

An Exceptionally Simple Theory of Everything - Preprint...

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Unformatted text preview: Preprint typeset in JHEP style - HYPER VERSION An Exceptionally Simple Theory of Everything A. Garrett Lisi SLRI, 722 Tyner Way, Incline Village, NV 89451 E-mail: alisi@hawaii.edu Abstract: All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold. Keywords: ToE . arXiv:0711.0770v1 [hep-th] 6 Nov 2007 Contents 1 . Introduction 1 1.1 A connection with everything 2 2 . The Standard Model Polytope 4 2.1 Strong G 2 5 2.2 Graviweak F 4 8 2.2.1 Gravitational D 2 8 2.2.2 Electroweak D 2 10 2.2.3 Graviweak D 4 11 2.2.4 F 4 13 2.3 F 4 and G 2 together 14 2.4 E 8 16 2.4.1 New particles 21 2.4.2 E 8 triality 22 3 . Dynamics 23 3.1 Curvature 23 3.2 Action 25 3.2.1 Gravity 25 3.2.2 Other bosons 26 3.2.3 Fermions 27 4 . Summary 28 5 . Discussion and Conclusion 28 1. Introduction We exist in a universe described by mathematics. But which math? Although it is inter- esting to consider that the universe may be the physical instantiation of all mathematics,[ 1 ] there is a classic principle for restricting the possibilities: The mathematics of the universe should be beautiful. A successful description of nature should be a concise, elegant, unified mathematical structure consistent with experience. Hundreds of years of theoretical and experimental work have produced an extremely successful pair of mathematical theories describing our world. The standard model of parti- cles and interactions described by quantum field theory is a paragon of predictive excellence. – 1 – General relativity, a theory of gravity built from pure geometry, is exceedingly elegant and effective in its domain of applicability. Any attempt to describe nature at the foundational level must reproduce these successful theories, and the most sensible course towards unifica- tion is to extend them with as little new mathematical machinery as necessary. The further we drift from these experimentally verified foundations, the less likely our mathematics is to correspond with reality. In the absence of new experimental data, we should be very careful, accepting sophisticated mathematical constructions only when they provide a clear simplification. And we should pare and unite existing structures whenever possible. The standard model and general relativity are the best mathematical descriptions we have of our universe. By considering these two theories and following our guiding principles, we will be led to a beautiful unification....
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An Exceptionally Simple Theory of Everything - Preprint...

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