An Exceptionally Simple Theory of Everything
"An Exceptionally Simple Theory of Everything" is a physics preprint proposing a basis for a unified field theory, often referred to as "E8 Theory", which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything. The paper was posted to the physics arXiv by Antony Garrett Lisi on November 6, 2007, and was not submitted to a peer-reviewed scientific journal. The title is a pun on the algebra used, the Lie algebra of the largest "simple", "exceptional" Lie group, E8. The paper's goal is to describe how the combined structure and dynamics of all gravitational and Standard Model particle fields, including fermions, are part of the E8 Lie algebra.
The theory is presented as an extension of the grand unified theory program, incorporating gravity and fermions. In the paper, Lisi states that all three generations of fermions do not directly embed in E8 with correct quantum numbers and spins, but that they must be described via a triality transformation, noting that the theory is incomplete and that a correct description of the relationship between triality and generations, if it exists, awaits a better understanding.
The theory received accolades from a few physicists amid a flurry of media coverage, but also met with widespread skepticism.Scientific American reported in March 2008 that the theory was being "largely but not entirely ignored" by the mainstream physics community, with a few physicists picking up the work to develop it further. In a follow-up paper, Lee Smolin proposed a spontaneous symmetry breaking mechanism for obtaining the classical action in Lisi's model, and speculated on the path to its quantization. In July 2009, Jacques Distler and Skip Garibaldi published a critical paper in Communications in Mathematical Physics called "There is no 'Theory of Everything' inside E8", arguing that Lisi's theory, and a large class of related models, cannot work. They offer a direct proof that it is impossible to embed all three generations of fermions in E8, or to obtain even the one-generation Standard Model without the presence of an antigeneration. In response to Distler and Garibaldi's paper, Lisi argued in a new paper, "An Explicit Embedding of Gravity and the Standard Model in E8", peer reviewed and published in a conference proceedings, that Distler and Garibaldi's assumptions about fermion embeddings are incorrect and that the antigeneration is not by itself a problem sufficient to rule out the one-generation Standard Model. In July 2010, a group of mathematicians and physicists, including David Vogan, Garibaldi, and Lisi, met for a week-long conference in Banff to discuss the mathematics and physics related to the exceptional groups. In December 2010, Scientific American published a feature article on "A Geometric Theory of Everything", authored by Lisi and James Owen Weatherall. In May 2011, Lisi wrote an entry in the blog section of Scientific American addressing some of the criticism of his theory and how it had progressed, noting that the theory was still incomplete and made only tenuous predictions, with a precise description of the three generations of fermions and their masses remaining as the largest outstanding problem. In June 2015, Lisi posted a paper, "Lie Group Cosmology”, describing the geometry of E8 Theory as an extension of Cartan geometry, and providing a description of the three generations of fermions via triality, while not predicting their masses.
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