The Magic Star of Exceptional Periodicity

Truini, Piero; Rios, Michael; Marrani, Alessio

doi:10.48550/arxiv.1711.07881

Cited by 9 publications

(43 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, the magic star algebras occurring in exceptional periodicity allow for a natural way to generalize e 8(−24) that is distinct from the infinite-dimensional Kac-Moody algebras [157,183]. Given their apparent ability to describe a monstrous M-theory that adds fermions to bosonic M-theory [96], further work is warranted to study BSM physics in relation to brane dynamics similar to those studied in generalizations of M-theory, such as F-theory and beyond [81,95,109,[184][185][186].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Beyond the standard model with six-dimensional spacetime

Chester,

Rios,

Marrani

2020

Preprint

Self Cite

View full text Add to dashboard Cite

6D spacetime with SO(3, 3) symmetry is utilized to efficiently encode three generations of matter. A graviGUT model is generalized to a class of models that all contain three generations and Higgs boson candidates. Pati-Salam, SU (5), and SO(10) grand unified theories are found when a single generation is isolated. For example, a SO(4, 2) spacetime group may be used for conformal symmetry, AdS5 → dS4, or simply broken to SO(3, 1) of Minkowski space. Another class of models finds SO(2, 2) and can give AdS3.

show abstract

Section: Discussionmentioning

confidence: 99%

“…(1) [157] isolates six exceptional Jordan algebras surrounding e 62 . The Peirce decomposition of the exceptional Jordan algebra occurs when breaking from e 6 to so 10 , as shown in Eq.…”

mentioning

confidence: 99%

Beyond the standard model with six-dimensional spacetime

Chester,

Rios,

Marrani

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A number of research venues stems from the novel non-Lie, infinitely countable chains of finite dimensional generalizations of exceptional Lie algebras provided by Magic Star algebras, introduced in [EP1] and in the present paper, after the anticipation given in [TRM17]. We here list some of the developments which we plan to report on in the near future.…”

Section: Further Developmentsmentioning

confidence: 97%

“…In a forthcoming paper [EP4], we will investigate this matrix algebra further; we think that this is indeed a rank-3 T-algebra [Vi]. 8 ), we can state the following result (anticipated in [TRM17]): there exists an 1 a 2 projection of the Magic Star algebras (namely, of the corresponding generalized root lattice), such that a Magic Star structure persists, with suitable generalizations of rank-3 Jordan algebras J q 3 (given by the aforementioned HTalgebras) occurring on the tips of the persisting Magic Star! The Magic Star projection of Magic Star algebras is depicted in Fig.…”

Section: Ht-algebrasmentioning

confidence: 99%

Exceptional Periodicity and Magic Star Algebras. II : Gradings and HT-Algebras

Truini¹,

Marrani²,

Rios³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We continue the study of Exceptional Periodicity and Magic Star algebras, which provide non-Lie, countably infinite chains of finite dimensional generalizations of exceptional Lie algebras. We analyze the graded algebraic structures arising in the Magic Star projection, as well as the Hermitian part of rank-3 Vinberg's matrix algebras (which we dub HT-algebras), occurring on each vertex of the Magic Star.

show abstract

“…The spin factor1 α ⊕ 1 β ⊕ 16 of T 8,2 3(5.13) enjoys an enhancement from so 16 to so 17,1 Lorentz symmetry8 , and der T 8,2 3 = so 17[28]. Breaking the so 25 Lie algebra of massless little group in 26 + 1 with respect to so 17 , as well as its 4096 spinor (both encoded in the so-called "Magic Star algebra" f 3 4[27]), one obtains the decomposition f 3 4 := so 25 ⊕ 4096 = so 17 ⊕ so 8 ⊕ (17, 8 v ) ⊕ (256, 8 s ) ⊕ (256, 8 c ).…”

mentioning

confidence: 99%

Monstrous M-theory

Marrani,

Rios,

Chester

2020

Preprint

Self Cite

View full text Add to dashboard Cite

We define a D = 26 + 1 Monstrous, purely bosonic M-theory, whose massless spectrum, of dimension 196, 884, is acted upon by the Monster group. Upon reduction to D = 25 + 1, this gives rise to a plethora of non-supersymmetric, gravito-dilatonic theories, whose spectrum irreducibly splits under the Monster as 196, 884 = 1 ⊕ 196, 883, where the singlet is identified with the dilaton, and 196, 883 denotes the smallest non-trivial representation of the Monster. This clarifies the definition of the Monster as the automorphism of the Griess algebra, by showing that such an algebra is not merely a sum of unrelated spaces, but rather an algebra of massless states for a Monstrous M-theory, which includes Horowitz and Susskind's bosonic M-theory as a subsector. Remarkably, a certain subsector of Monstrous M-theory, when coupled to a Rarita-Schwinger massless field in 26 + 1, exhibits the same number of bosonic and fermionic degrees of freedom.

show abstract

The Magic Star of Exceptional Periodicity

Cited by 9 publications

References 0 publications

Beyond the standard model with six-dimensional spacetime

Beyond the standard model with six-dimensional spacetime

Exceptional Periodicity and Magic Star Algebras. II : Gradings and HT-Algebras

Monstrous M-theory

Contact Info

Product

Resources

About