A closer look at the Higgs vacuum and a model of sporadic groups

TL;DR

This paper explores the Higgs vacuum's finite symmetry, proposing it as the Fisher-Griess monster group, and links sporadic groups to elementary particle symmetries through advanced mathematical and physical theories.

Contribution

It introduces a novel connection between the Higgs vacuum, sporadic groups, and string theory, proposing the monster group as a fundamental symmetry in particle physics.

Findings

Finite Higgs vacuum symmetry is the Fisher-Griess monster group.

Mass scales correspond to unbroken and broken monster symmetries.

Connections between the j-function, zeta zeros, and phase transitions are established.

Abstract

Analyzing the vacuum of the Higgs field reveals that it must have a finite symmetry. It is proposed that this finite symmetry is the Fisher-Griess monster $\mathbb{M}$ symmetry. Particularly, it is reported that the initial state of an unbroken $\mathbb{M}\times \mathbb{M}$ supersymmetry produces a mass of $1.1 \times 10^{19}$ GeV whereas the final state of a fully-broken $\mathbb{M}\times \mathbb{M}$ produces 125.4 GeV (comparable to the Planck scale $1.2 \times 10^{19}$ GeV and the Higgs boson (electroweak) scale 125.1 GeV). Also, it is shown that breaking $Weyl(E_8)\times Weyl(E_8)$ supersymmetry yields a scale of $4.4 \times 10^{16} \rm\:$GeV (comparable to the GUT scale of $2 \times 10^{16} \rm\:$GeV). Based on such evidence, therefore, the monster CFT partition function (i.e., modular invariant j-function) and the monster SCFT partition function are addressed. Next, by the Lee-Young theory, the phase transition with spontaneous symmetry breaking in the model, due to the condensation of zeros of the partition function along the unit circle, is explained. Afterward, addressing the well-known connection between the j-function and the Riemann zeta function, a match between the critical temperature of the model and the Boltzmann factor (fugacity) corresponding to the first nontrivial zero of the zeta function is reported (i.e., $T^{\ast}\cong e^{i \pi \zeta_1}$) and interpreted. Then, noting the evidence of a $\mathbb{M}$ symmetry for the Higgs field, first, the massless Photon is introduced as its trivial centralizer (the identity element $\mathbb{1}$). Finally, based on some relationships in the sporadic groups, the other 25 sporadic groups are suggested as the symmetries for the fields of 25 elementary particles (including the graviton and another particle, seemingly a leptoquark).