There is No “Theory of Everything” Inside E8

@article{Distler2009ThereIN,
  title={There is No “Theory of Everything” Inside E8},
  author={Jacques Distler and Skip Garibaldi},
  journal={Communications in Mathematical Physics},
  year={2009},
  volume={298},
  pages={419-436}
}
We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any “Theory of Everything” obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras in the spirit of Dynkin’s classic papers and are written for mathematicians. 
An Explicit Embedding of Gravity and the Standard Model in E8
The algebraic elements of gravitational and Standard Model gauge fields acting on a generation of fermions may be represented using real matrices. These elements match a subalgebra of spin(11,3)
The GraviGUT Algebra Is not a Subalgebra of E8, but E8 Does Contain an Extended GraviGUT Algebra
The (real) GraviGUT algebra is an extension of the spin(11;3) algebra by a 64- dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed
Exceptional lie algebras at the very foundations of space and time
While describing the results of our recent work on exceptional Lie and Jordan algebras, so tightly intertwined in their connection with elementary particles, we will try to stimulate a critical
Part 2: Zorn-type Representations
A representation of the exceptional Lie algebras reecting a simple unifying view, based on realizations in terms of Zorn-type matrices, is presented. The role of the underlying Jordan pair and Jordan
Exceptional Lie algebras, SU(3) and Jordan pairs: part 2. Zorn-type representations
A representation of the exceptional Lie algebras reflecting a simple unifying view, based on realizations in terms of Zorn-type matrices, is presented. The role of the underlying Jordan pair and
The magic star of exceptional periodicity
We present a periodic infinite chain of finite generalisations of the exceptional structures, including e8, the exceptional Jordan algebra (and pair), and the octonions. We demonstrate that the
$E_8$, the most exceptional group
The five exceptional simple Lie algebras over the complex number are included one within the other as $G_2 \subset F_4 \subset E_6 \subset E_7 \subset E_8$. The biggest one, $E_8$, is in many ways
Exceptional Periodicity and Magic Star Algebras. I : Foundations
We introduce and start investigating the properties of countably infinite, periodic chains of finite dimensional generalizations of the exceptional Lie algebras: each exceptional Lie algebra (but
Space, Matter and Interactions in a Quantum Early Universe Part I: Kac-Moody and Borcherds Algebras
We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and
Gravity and unification: a review
We review various classical unified theories of gravity and other interactions that have appeared in the literature, paying special attention to scenarios in which spacetime remains four-dimensional,
...
1
2
3
...

References

SHOWING 1-10 OF 60 REFERENCES
An Exceptionally Simple Theory of Everything
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
Lie groups and Lie algebras
From the reviews of the French edition "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular
Finite groups of Lie type: Conjugacy classes and complex characters
BN-Pairs and Coxeter Groups. Maximal Tori and Semisimple Classes. Geometric Conjugacy and Duality. Unipotent Classes. The Steinberg Character. The Generalized Characters of Deligne-Lusztig. Further
On exceptional nilpotents in semisimple Lie algebras
We classify all pairs (m,e), where m is a positive integer and e is a nilpotent element of a semisimple Lie algebra, which arise in the classification of simple rational W-algebras.
Introduction to Lie Algebras and Representation Theory
Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-
Do It Yourself: the Structure Constants for Lie Algebras of Types El
Two algorithms for computing the structure table of Lie algebras of type El with respect to a Chevalley base are compared: the usual inductive algorithm and an algorithm based on the use of the
Clifford algebras of hyperbolic involutions
Abstract. For $\As$ a central simple algebra of even degree with hyperbolic orthogonal involution, we describe the canonically induced involution ${\underline \sigma}$ on the even Clifford algebra
Differential Geometry, Lie Groups, and Symmetric Spaces
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric
Gauged N=4 supergravities
We present the gauged N = 4 (half-maximal) supergravities in four and five spacetime dimensions coupled to an arbitrary number of vector multiplets. The gaugings are parameterized by a set of
...
1
2
3
4
5
...