On possible embeddings of the standard model of particle physics and gravity in $E_8$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909190531842048 |
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| author | Wilson, Robert A. |
| author_facet | Wilson, Robert A. |
| contents | I investigate the structure of $E_8$ under the action of the subalgebra/subgroup $A_1+G_2+C_3$, as a potential route to unification of the fundamental forces of nature into a single algebraic structure. The particular real form $E_{8(-24)}$ supports a decomposition into compact $G_2$ plus split $A_1+C_3$, which allows a restriction from $G_2$ to $SU(3)$ for the strong force, together with split $SL_2(\mathbb R)$ to break the symmetry of the weak interaction and give mass to the intermediate vector bosons. The factor $C_3$ contains various copies of the Lorentz group $SL_2(\mathbb C)$ and extends the `spacetime' symmetries to the full group of symplectic symmetries of real $3+3$-dimensional phase space.
Restricting $G_2$ to the Standard Model $SU(3)$ extends $C_3$ to $A_5$, in the real form $SU(3,3)$, acting on a complex phase space that includes both momentum and current. There is then a natural restriction from $SU(3,3)$ to $SO(3,3)$, describing the action of $SL_4(\mathbb R)$ on phase space. The resulting action of $SL_4(\mathbb R)$ on $E_8$ includes tensors that are equivalent to the stress-energy tensor, the Ricci tensor and the Riemann tensor, and therefore permits the formalism of general relativity to be developed inside $E_{8(-24)}$. The model then suggests unexpected and perhaps subtle ways in which general relativity and particle physics may be forced to modify each other, in order to produce a unified theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On possible embeddings of the standard model of particle physics and gravity in $E_8$ Wilson, Robert A. General Physics High Energy Physics - Phenomenology I investigate the structure of $E_8$ under the action of the subalgebra/subgroup $A_1+G_2+C_3$, as a potential route to unification of the fundamental forces of nature into a single algebraic structure. The particular real form $E_{8(-24)}$ supports a decomposition into compact $G_2$ plus split $A_1+C_3$, which allows a restriction from $G_2$ to $SU(3)$ for the strong force, together with split $SL_2(\mathbb R)$ to break the symmetry of the weak interaction and give mass to the intermediate vector bosons. The factor $C_3$ contains various copies of the Lorentz group $SL_2(\mathbb C)$ and extends the `spacetime' symmetries to the full group of symplectic symmetries of real $3+3$-dimensional phase space. Restricting $G_2$ to the Standard Model $SU(3)$ extends $C_3$ to $A_5$, in the real form $SU(3,3)$, acting on a complex phase space that includes both momentum and current. There is then a natural restriction from $SU(3,3)$ to $SO(3,3)$, describing the action of $SL_4(\mathbb R)$ on phase space. The resulting action of $SL_4(\mathbb R)$ on $E_8$ includes tensors that are equivalent to the stress-energy tensor, the Ricci tensor and the Riemann tensor, and therefore permits the formalism of general relativity to be developed inside $E_{8(-24)}$. The model then suggests unexpected and perhaps subtle ways in which general relativity and particle physics may be forced to modify each other, in order to produce a unified theory. |
| title | On possible embeddings of the standard model of particle physics and gravity in $E_8$ |
| topic | General Physics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2404.18938 |