http://www.arxiv.org/pdf/0711.0770
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 united
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.
1. Introduction
[...]
Hundreds of years of theoretical and experimental work have produced
an extremely successful pair of mathematical theories describing our
world. The standard model of particles and interactions described by
quantum field theory is a paragon of predictive excellence.
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 unification 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.
Contents [page]
1. Introduction 1
1.1 A connection with everything 2
2. The Standard Model Polytope 4
2.1 Strong G2 5
2.2 Graviweak F4 8
2.2.1 Gravitational D2 8
2.2.2 Electroweak D2 10
2.2.3 Graviweak D4 11
2.2.4 F4 13
2.3 F4 and G2 together 14
2.4 E8 16
2.4.1 New particles 21
2.4.2 E8 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
See the whole text article here:
http://www.arxiv.org/pdf/0711.0770 
