# 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.

## 26 Citations

An Explicit Embedding of Gravity and the Standard Model in E8

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The GraviGUT Algebra Is not a Subalgebra of E8, but E8 Does Contain an Extended GraviGUT Algebra

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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
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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

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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

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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

- Mathematics, PhysicsSymmetry
- 2021

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

- PhysicsClassical and Quantum Gravity
- 2018

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,…

## References

SHOWING 1-10 OF 60 REFERENCES

An Exceptionally Simple Theory of Everything

- Mathematics
- 2007

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

- Mathematics
- 1998

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

- Mathematics
- 1985

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

- Mathematics
- 2008

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

- Mathematics
- 1973

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

- Mathematics
- 2004

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

- Mathematics
- 2001

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

- Mathematics
- 1978

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

- Physics
- 2006

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…