arXiv subjects

M. J. Hughes

Publications and source records attributed to M. J. Hughes.

6 recordsLinked to original sources

arXiv2024

Three Generations and a Trio of Trialities

We identify the Standard Model's $\mathfrak{su}(3)\oplus \mathfrak{su}(2)\oplus \mathfrak{u}(1)$ internal symmetries within the triality symmetries $\mathfrak{tri}(\mathbb{C}) \oplus \mathfrak{tri}(\mathbb{H}) \oplus \mathfrak{tri}(\mathbb{O})$. From here, the corresponding Standard Model group action is applied to the triality triple $\left( Ψ_+, Ψ_-,V\right)$ for $Ψ_+, Ψ_-, V \in \mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$. Together, $Ψ_+$ and $Ψ_-$ provide the correct irreducible representations for two generations. Owing to a certain Cartan Factorization, which we define, $V$ provides the irreducible representations for a third generation. Said more explicitly in another way, division algebraic multiplication merges a third generation of spinor representations into a set of scalar bosons. This set of scalar bosons includes the familiar Standard Model Higgs representation.

hep-ph↗

arXiv2022

Division algebraic symmetry breaking

Reframing certain well-known particle models in terms of normed division algebras leads to two new results for BSM physics. (1) We identify a sequence of complex structures which induces a cascade of breaking symmetries: Spin(10) $\mapsto$ Pati-Salam $\mapsto$ Left-Right symmetric $\mapsto$ Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers. (2) We provide, also for the first time we believe, an explicit demonstration of left-right symmetric Higgs representations stemming from quaternionic triality, tri($\mathbb{H}$). Upon the breaking of $su(2)_R$, our Higgs reduces to the familiar standard model Higgs.

hep-ph↗

arXiv2022

One generation of standard model Weyl representations as a single copy of $\mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$

Peering in from the outside, $\mathbb{A} := \mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$ looks to be an ideal mathematical structure for particle physics. It is 32 $\mathbb{C}$-dimensional: exactly the size of one full generation of fermions. Furthermore, as alluded to earlier in arXiv:1806.00612, it supplies a richer algebraic structure, which can be used, for example, to replace SU(5) with the SU(3)$\times$SU(2)$\times$U(1) / $\mathbb{Z}_6$ symmetry of the standard model. However, this line of research has been weighted down by a difficulty known as the fermion doubling problem. That is, a satisfactory description of SL(2,$\mathbb{C}$) symmetries has so far only been achieved by taking two copies of the algebra, instead of one. Arguably, this doubling of states betrays much of $\mathbb{A}$'s original appeal. In this article, we solve the fermion doubling problem in the context of $\mathbb{A}$. Furthermore, we give an explicit description of the standard model symmetries, $g_{sm}$, its gauge bosons, Higgs, and a generation of fermions, each in the compact language of this 32 $\mathbb{C}$-dimensional algebra. Most importantly, we seek out the subalgebra of $g_{sm}$ that is invariant under the complex conjugate - and find that it is given by $su(3)_C \oplus u(1)_{EM}$. Could this new result provide a clue as to why the standard model symmetries break in the way that they do?

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arXiv2016

Twin Supergravities from Yang-Mills Squared

We consider `twin supergravities' - pairs of supergravities with $\mathcal{N}_+$ and $\mathcal{N}_-$ supersymmetries, $\mathcal{N}_+>\mathcal{N}_-$, with identical bosonic sectors - in the context of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of twin supergravity theories are related through their left and right super Yang-Mills factors. This procedure generates new theories from old. In particular, the matter coupled $\mathcal{N}_-$ twins in $D=3,5,6$ and the $\mathcal{N}_-=1$ twins in $D=4$ have not, as far as we are aware, been obtained previously using the double-copy construction, adding to the growing list of double-copy constructible theories. The use of fundamental matter multiplets in the double-copy construction leads us to introduce a bi-fundamental scalar that couples to the well-known bi-adjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorisation into left and right super Yang-Mills-matter theories.

hep-th↗

arXiv2016

Global symmetries of Yang-Mills squared in various dimensions

Tensoring two on-shell super Yang-Mills multiplets in dimensions $D\leq 10$ yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) $\mathbb{D}$ with each dimension $3\leq D\leq 10$ we obtain formulae for the algebras $\mathfrak{g}$ and $\mathfrak{h}$ of the U-duality group $G$ and its maximal compact subgroup $H$, respectively, in terms of the internal global symmetry algebras of each super Yang-Mills theory. We extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product.

hep-th↗

arXiv2015

Octonionic D=11 Supergravity and 'Octavian Integers' as Dilaton Vectors

We formulate D=11 supergravity over the octonions by rewriting 32-component Majorana spinors as 4-component octonionic spinors. Dimensional reduction to D=4 and D=3 suggests an interpretation of the so-called 'dilaton vectors', which parameterise the couplings of the dilatons to other fields in the theory, as unit 'octavian integers' - the octonionic analogues of integers. The parameterisation involves a novel use of the duality between points and lines on the Fano plane, and suggests a series of consistent truncations with N=8,4,2,1, giving the 'four curious supergravities' studied by Duff and Ferrara

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