arXiv subjects

Michael Rios

Publications and source records attributed to Michael Rios.

At least 19 recordsLinked to original sources

arXiv2024

Flipped $SU(5)$ GUT with conformal gravity from a single supermultiplet

The Grassmann envelope is used to find the $\mathcal{N}=1$ `superquasiconformal' algebra in $D=10+1$. The adjoint representation of this algebra is found to contain $\mathfrak{su}_{2,2}\oplus \mathfrak{u}_{1}\oplus \mathfrak{su}_{5}$ as a submaximal subalgebra, giving a spectrum of conformal gravity with flipped $SU_{5}\times U_{1}$ GUT. Combining Yang-Mills theory with MacDowell-Mansouri gravity over the conformal group is found to recover the Einstein-Hilbert action with a cosmological constant. An action for the theory is presented, which contains the gauge bosons of gravity and GUT, three generations of fermions in an efficient manner, and a new Higgs sector. By using the superalgebra for the entire multiplet, the theory gauges a non-supersymmetric subalgebra without introducing superpartners.

hep-th↗

arXiv2022

Warm Dark Matter from Higher-Dimensional Gauge Theories

Warm dark matter particles with masses in the keV range have been linked with the large group representations in gauge theories through a high number of species at decoupling. In this paper, we address WDM fermionic degrees of freedom from such representations. Bridging higher-dimensional particle physics theories with cosmology studies and astrophysical observations, our approach is two-folded, i.e., it includes realistic models from higher-dimensional representations and constraints from simulations tested against observations. Starting with superalgebras in exceptional periodicity theories, we discuss several symmetry reductions and we consider several representations that accommodate a high number of degrees of freedom. We isolate a model that naturally accommodates both the standard model representation and the fermionic dark matter in agreement with both large and small-scale constraints. This model considers an intersection of branes in $D=27+3$ in a manner that provides the degrees of freedom for the standard model on one hand and 2048 fermionic degrees of freedom for dark matter, corresponding to a $\sim$2 keV particle mass, on the other. In this context, we discuss the theoretical implications and the observable predictions.

astro-ph.CO↗

arXiv2020

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 creation driven by algebraic extensions of the Kac-Moody Lie algebra $\mathbf{e_9}$. We investigate Kac-Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.

gr-qc↗

arXiv2020

Space, Matter and Interactions in a Quantum Early Universe. Part II : Superalgebras and Vertex Algebras

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra $\textbf{${\mathfrak g}_{\mathsf u}$}$ that extends $\mathbf{e_9}$. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn $\textbf{${\mathfrak g}_{\mathsf u}$}$ into a Lie superalgebra $\textbf{$\mathfrak {sg}_{\mathsf u}$}$ with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincar\'e group on $\textbf{$\mathfrak {sg}_{\mathsf u}$}$, which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular {\it resonant scattering}. Finally, we complete the model by merging the local $\textbf{$\mathfrak {sg}_{\mathsf u}$}$ into a vertex-type algebra.

gr-qc↗

arXiv2020

Monstrous M-theory

In $26+1$ space-time dimensions, we introduce a gravity theory whose massless spectrum can be acted upon by the Monster group when reduced to $25+1$ dimensions. This theory generalizes M-theory in many respects and we name it Monstrous M-theory, or M$^{2}$-theory. Upon Kaluza-Klein reduction to $25+1$ dimensions, the M$^{2}$-theory spectrum irreducibly splits as $\mathbf{1}\oplus\mathbf{196,883}$, where $\mathbf{1}$ is identified with the dilaton, and $\mathbf{196,883}$ is the dimension of the smallest non-trivial representation of the Monster. This provides a field theory explanation of the lowest instance of the Monstrous Moonshine, and it clarifies the definition of the Monster as the automorphism group of the Griess algebra, by showing that such an algebra is not merely a sum of unrelated spaces, but descends from massless states for M$^{2}$-theory, which includes Horowitz and Susskind's bosonic M-theory as a subsector. Further evidence is provided by the decomposition of the coefficients of the partition function of Witten's extremal Monster SCFT in terms of representations of $SO_{24}$, the massless little group in $25+1$; the purely bosonic nature of the involved $SO_{24}$-representations may be traced back to the unique feature of $24$ dimensions, which allow for a non-trivial generalization of the triality holding in $8$ dimensions. Last but not least, a certain subsector of M$^{2}$-theory, when coupled to a Rarita-Schwinger massless field in $26+1$, exhibits the same number of bosonic and fermionic degrees of freedom; we cannot help but conjecture the existence of a would-be $\mathcal{N}=1$ supergravity theory in $26+1$ space-time dimensions.

hep-th↗

arXiv2020

Beyond the standard model with six-dimensional spinors

6D spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati-Salam, $SU(5)$, and $Spin(10)$ grand unified theories are found when a single generation is isolated. For spacetime symmetries, $Spin(4,2)$ may be used for conformal symmetry, $AdS_5\rightarrow dS_4$, or simply broken to $Spin(3,1)$ of Minkowski space. Another class of representations finds $Spin(2,2)$ and can give $AdS_3$ with various GUTs. An action for three generations of fermions in the Majorana-Weyl spinor ${\bf 128}$ of $Spin(4,12)$ is found with $Spin(3)$ flavor symmetry inside $E_{8(-24)}$. The ${\bf 128}$ of $Spin(4,12)$ can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane $E_{8(-24)}/Spin(4,12)= (\mathbb{O}_s\times\mathbb{O})\mathbb{P}^2$.

physics.gen-ph↗

arXiv2019

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

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.

math.RT↗

arXiv2019

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 $\mathbf{g}_{2}$) is part of an infinite family of finite dimensional algebras, which we name "Magic Star" algebras. These algebras have remarkable similarities with many characterizing features of the exceptional Lie algebras.

math.RT↗

arXiv2019

Exceptional Super Yang-Mills in $D=27+3$ and Worldvolume M-Theory

Bars and Sezgin have proposed a super Yang-Mills theory in $D=s+t=11+3$ space-time dimensions with an electric 3-brane that generalizes the 2-brane of M-theory. More recently, the authors found an infinite family of exceptional super Yang-Mills theories in $D=(8n+3)+3$ via the so-called Magic Star algebras. A particularly interesting case occurs in signature $D=27+3$, where the superalgebra is centrally extended by an electric 11-brane and its 15-brane magnetic dual. The worldvolume symmetry of the 11-brane has signature $D=11+3$ and can reproduce super Yang-Mills theory in $D=11+3$. Upon reduction to $D=26+2$, the 11-brane reduces to a 10-brane with $10+2$ worldvolume signature. A single time projection gives a $10+1$ worldvolume signature and can serve as a model for $D=10+1$ M-theory as a reduction from the $D=26+1$ signature of the bosonic M-theory of Horowitz and Susskind; this is further confirmed by the reduction of chiral $(1,0)$, $D=11+3$ superalgebra to the $\mathcal{N}=1$ superalgebra in $D=10+1$, as found by Rudychev, Sezgin and Sundell some time ago. Extending previous results of Dijkgraaf, Verlinde and Verlinde, we also put forward the realization of spinors as total cohomologies of (the largest spatially extended) branes which centrally extend the $(1,0)$ superalgebra underlying the corresponding exceptional super Yang-Mills theory. Moreover, by making use of an "anomalous" Dynkin embedding, we strengthen Ramond and Sati's argument that M-theory has hidden Cayley plane fibers.

hep-th↗

arXiv2018

The Magic of Being Exceptional

Starting from the Jordan algebraic interpretation of the "Magic Star" embedding within the exceptional sequence of simple Lie algebras, we exploit the so-called spin factor embedding of rank-3 Jordan algebras and its consequences on the Jordan algebraic Lie symmetries, in order to provide another perspective on the origin of the "Exceptional Periodicity" (EP) and its "Magic Star" structure. We also highlight some properties of the special class of Vinberg's rank-3 (dubbed exceptional) T-algebras, appearing on the tips of the "Magic Star" projection of EP(-generalized, finite-dimensional, exceptional) algebras.

hep-th↗

arXiv2018

Magic Star and Exceptional Periodicity: an approach to Quantum Gravity

We present a periodic infinite chain of finite generalisations of the exceptional structures, including the exceptional Lie algebra $\mathbf{e_8}$, the exceptional Jordan algebra (and pair) and the octonions. We will also argue on the nature of space-time and indicate how these algebraic structures may inspire a new way of going beyond the current knowledge of fundamental physics.

hep-th↗

arXiv2018

The Geometry of Exceptional Super Yang-Mills Theories

Some time ago, Sezgin, Bars and Nishino have proposed super Yang-Mills theories (SYM's) in $D=11+3$ and beyond. Using the "Magic Star" projection of $\mathfrak{e}_{8(-24)}$, we show that the geometric structure of SYM's in $11+3$ and $12+4$ space-time dimensions is recovered from the affine symmetry of the space $AdS_{4}\otimes S^{8}$, with the $8$-sphere being a line in the Cayley plane. By reducing to transverse transformations, along maximal embeddings, the near horizon geometries of the M2-brane ($AdS_{4}\otimes S^{7}$) and M5-brane ($AdS_{7}\otimes S^{4}$) are recovered. Generalizing the construction to higher, generic levels of the recently introduced "Exceptional Periodicity" (EP) and exploiting the embedding of semi-simple rank-3 Jordan algebras into rank-3 T-algebras of special type, yields the spaces $AdS_{4}\otimes S^{8n}$ and $AdS_{7}\otimes S^{8n-3}$, with reduced subspaces $AdS_{4}\otimes S^{8n-1}$ and $AdS_{7}\otimes S^{8n-4}$, respectively. Within EP, this suggests generalizations of the near horizon geometry of the M2-brane and its Hodge (magnetic) duals, related to $(1,0)$ SYM's in $(8n+3)+3$ dimensions, constituting a particular class of novel higher-dimensional SYM's, which we name exceptional SYM's. Remarkably, the $n=3$ level gives $AdS_{4}\otimes S^{23}$, hinting at M2 and M21 branes as solutions of bosonic M-theory, and reduction to $AdS_{3}\otimes S^{23}$ gives support for Witten's monstrous $AdS$/CFT construction.

hep-th↗

arXiv2017

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 exceptional Jordan algebra is part of an infinite family of finite-dimensional matrix algebras (corresponding to a particular class of cubic Vinberg's T-algebras). Correspondingly, we prove that e8 is part of an infinite family of algebras (dubbed "Magic Star" algebras) that resemble lattice vertex algebras.

hep-th↗

arXiv2015

On a Final Theory of Mathematics and Physics

Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is mounting evidence this ultimate theory of physics will also be a unified theory of mathematics.

physics.hist-ph↗

arXiv2013

U-Duality and the Leech Lattice

It has recently been shown that the full automorphism group of the Leech lattice, Conway's group Co_0, can be generated by 3 x 3 matrices over the octonions. We show such matrices are of type F_4 in E_{6(-26)}, the U-duality group for N=2, D=5 exceptional magic supergravity. By mapping points of the Leech lattice to black hole charge vectors, it is seen Co_0 is generated by U-duality transformations acting as rotations in the charge space for BPS black holes.

hep-th↗

arXiv2012

Extremal Black Holes as Qudits

We extend the black hole/qudit correspondence by identifying five and six-dimensional 1/2-BPS black string and hole charge vectors in N=8 and N=2 magic supergravities with qubits and qutrits over composition algebras. In D=6, this is accomplished via Hopf fibrations, which map qubits over composition algebras to rank one elements of Jordan algebras of degree two. An analogous procedure maps qutrits over composition algebras to D=5 charge vectors, which are rank one elements of Jordan algebras of degree three. In both cases, the U-duality groups are interpreted as qudit SLOCC transformation groups. We provide explicit gates for such transformations and study their applications in toroidally compactified M-theory.

hep-th↗

arXiv2010

Jordan C*-Algebras and Supergravity

It is known that black hole charge vectors of N=8 and magic N=2 supergravity in four and five dimensions can be represented as elements of Jordan algebras of degree three over the octonions and split-octonions and their Freudenthal triple systems. We show both such Jordan algebras are contained in the exceptional Jordan C*-algebra and construct its corresponding Freudenthal triple system and single variable extension. The transformation groups for these structures give rise to the complex forms of the U-duality groups for N=8 and magic N=2 supergravities in three, four and five dimensions.

hep-th↗

arXiv2007

Jordan Algebras and Extremal Black Holes

We review various properties of the exceptional Euclidean Jordan algebra of degree three. Euclidean Jordan algebras of degree three and their corresponding Freudenthal triple systems were recently shown to be intimately related to extremal black holes in N=2, d=4 homogeneous supergravities. Using a novel type of eigenvalue problem with eigenmatrix solutions, we elucidate the rich matrix geometry underlying the exceptional N=2, d=4 homogeneous supergravity and explore the relations to extremal black holes.

hep-th↗