An exceptional G(2) extension of the Standard Model from the correspondence with Cayley–Dickson algebras automorphism groups

Abstract

In this article I propose a new criterion to extend the Standard Model of particle physics from a straightforward algebraic conjecture: the symmetries of physical microscopic forces originate from the automorphism groups of main Cayley–Dickson algebras, from complex numbers to octonions and sedenions. This correspondence leads to a natural enlargement of the Standard Model color sector, from a SU(3) gauge group to an exceptional Higgs-broken G(2) group, following the octonionic automorphism relation guideline. In this picture, an additional ensemble of massive G(2)-gluons emerges, which is separated from the particle dynamics of the Standard Model.

An exceptional G(2) extension of the Standard Model from an algebraic conjecture: implications for the strong sector and dark matter

“…In our case, the six dark gluons can form dark glueballs constituted by two or three (or multiples) 𝐺 (2) gluons, according to {14} ⊗ {14} = {1} ⊕ ... and {14} ⊗ {14} ⊗ {14} = {1} ⊕ ... representations [36], with integer total angular momentum 𝐽 = 0, 2 and 𝐽 = 1, 3 for 2-gluons and 3-gluons balls respectively. In principle, exceptional-colored broken-𝐺 (2) glueballs should not be stable and we have to introduce a stabilizing feature, such as an accidental symmetry, a global discrete 𝑍 2 (or 𝑍 𝑁 ) symmetry or 𝐺-parity conservation for a generic Yang-Mills [23]. From a cosmological point of view, the usual WIMP-like scenario built via the freeze-out mechanism cannot be achieved, since these gluons/glueballs are never in thermal equilibrium with the baryon-photon fluid in the early Universe: we have to invoke a FIMP scenario and a SIMP Dark freez-out with number changing processes applied to an exotic Higgs-portal (see [23] for a complete dissertation).…”

“…In principle, exceptional-colored broken-𝐺 (2) glueballs should not be stable and we have to introduce a stabilizing feature, such as an accidental symmetry, a global discrete 𝑍 2 (or 𝑍 𝑁 ) symmetry or 𝐺-parity conservation for a generic Yang-Mills [23]. From a cosmological point of view, the usual WIMP-like scenario built via the freeze-out mechanism cannot be achieved, since these gluons/glueballs are never in thermal equilibrium with the baryon-photon fluid in the early Universe: we have to invoke a FIMP scenario and a SIMP Dark freez-out with number changing processes applied to an exotic Higgs-portal (see [23] for a complete dissertation). Possible manifestations of 𝐺 (2) gluons in the present Universe are massive boson stars with repulsive quartic self-interaction potential: this heavy 𝐺 (2) gluon dark matter is indeed capable of producing stellar objects, which could populate the dark halos [23].…”

“…This is a strong hint that the Naturalness criterion for the Higgs sector and the so-called WIMP Miracle [38] could not be a prerogative of Nature. We propose an approach based on a division algebras conjecture capable of selecting a unique extension of the SM, which introduces a branch of exceptional matter particles from a simple and minimally high symmetry [23]: fundamental interactions are identified with the automorphism groups of Cayley-Dickson algebras. From the automorphism of octonions (and sedenions) algebra, the promising exceptional symmetry group 𝐺 (2) can be pinpointed to solve the DM problem.…”

Explicit Multiplication Tables of Cayley-Dickson Algebras

“…Cayley-Dickson algebras have shown great influences in physics and mathematics, for instances on algebras [15], analysis [9], geometry [11,16], quantum field theory [7,4], and the standard model of the universe [10]. There is an urgent need for explicit multiplication tables.…”

Listening to Celestial Algebras

“…With a little help from E. Cartan[6] 3. Of course, this has not prevented to find physical applications for the sedenions as recently explored in e.g.,[8].…”