GraviGUT unification with revisited Pati-Salam model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915551054397440 |
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| author | Alexander, Stephon Alexandre, Bruno Fine, Michael Magueijo, João Nākums, Edžus |
| author_facet | Alexander, Stephon Alexandre, Bruno Fine, Michael Magueijo, João Nākums, Edžus |
| contents | We propose a graviGUT unification scheme based on the simple orthogonal group $\mathrm{SO}(1,9 ,\mathbb{C})$ that resolves the chiral duplication of weak isospin in Pati--Salam models. In the conventional $SU(4)\times SU(2)_+\times SU(2)_-$ framework, the unobserved second chiral $SU(2)$ is typically removed by ad hoc high-energy scale breaking. Here we instead \emph{geometrize} it: one $SU(2)$ factor is identified with a chiral half of the Lorentz group, so it belongs to gravity rather than to an additional weak force. This identification becomes natural inside $\mathrm{SO}(1,9 ,\mathbb{C})$, where the algebra decomposes as $\mathfrak{so}(1,3)_{\mathbb{C}}\oplus\mathfrak{so}(6)_{\mathbb{C}}\oplus(\text{coset})$. We construct a parity-symmetric chiral action that, upon breaking \emph{dynamically} selects one chirality: the surviving Yang--Mills factor is identified with $SU(2)_+$, while the opposite chirality persists as the gravitational chiral connection. These lead to concrete phenomenological handles, including graviton and weak-boson vertices with the other fundamental forces in $SU(3)$ and $U(1)$ and parity-sensitive gravitational-wave signatures, that distinguish the $\mathrm{SO}(1,9,\mathbb{C})$ construction from both traditional Pati--Salam and larger, less economical unifications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_11674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GraviGUT unification with revisited Pati-Salam model Alexander, Stephon Alexandre, Bruno Fine, Michael Magueijo, João Nākums, Edžus High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We propose a graviGUT unification scheme based on the simple orthogonal group $\mathrm{SO}(1,9 ,\mathbb{C})$ that resolves the chiral duplication of weak isospin in Pati--Salam models. In the conventional $SU(4)\times SU(2)_+\times SU(2)_-$ framework, the unobserved second chiral $SU(2)$ is typically removed by ad hoc high-energy scale breaking. Here we instead \emph{geometrize} it: one $SU(2)$ factor is identified with a chiral half of the Lorentz group, so it belongs to gravity rather than to an additional weak force. This identification becomes natural inside $\mathrm{SO}(1,9 ,\mathbb{C})$, where the algebra decomposes as $\mathfrak{so}(1,3)_{\mathbb{C}}\oplus\mathfrak{so}(6)_{\mathbb{C}}\oplus(\text{coset})$. We construct a parity-symmetric chiral action that, upon breaking \emph{dynamically} selects one chirality: the surviving Yang--Mills factor is identified with $SU(2)_+$, while the opposite chirality persists as the gravitational chiral connection. These lead to concrete phenomenological handles, including graviton and weak-boson vertices with the other fundamental forces in $SU(3)$ and $U(1)$ and parity-sensitive gravitational-wave signatures, that distinguish the $\mathrm{SO}(1,9,\mathbb{C})$ construction from both traditional Pati--Salam and larger, less economical unifications. |
| title | GraviGUT unification with revisited Pati-Salam model |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2510.11674 |