# 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.

## 29 Citations

### An Explicit Embedding of Gravity and the Standard Model in E8

- Physics
- 2010

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

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- 2014

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

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- 2015

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### Part 2: Zorn-type Representations

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- 2014

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

- Mathematics
- 2011

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

- MathematicsNonassociative Mathematics and its Applications
- 2019

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

- Mathematics
- 2016

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

- Mathematics
- 2019

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…

### Octions: An E8 description of the Standard Model

- MathematicsJournal of Mathematical Physics
- 2022

We interpret the elements of the exceptional Lie algebra [Formula: see text] as objects in the Standard Model, including lepton and quark spinors with the usual properties, the Standard Model Lie…

### 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…

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