Holomorphic Unified Field Theory of Gravity and the Standard Model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911276744048640 |
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| author | Moffat, John. W. Thompson, Ethan. J. |
| author_facet | Moffat, John. W. Thompson, Ethan. J. |
| contents | We present a holomorphic framework in which gravity, gauge interactions, and their couplings to charges and currents emerge from a single geometric action on a four-complex-dimensional manifold. The Hermitian metric yields on the real slice $y^μ= 0$, a real symmetric metric $g_{(μν)}$ giving the vacuum Einstein equations, and an antisymmetric part $g_{[μν]}$ that reproduces Maxwell's equations with sources. A single holomorphic gauge connection for $G_{\text{GUT}}$, such as $SU(5)$ or $SO(10)$, encodes all gauge sectors; its Bianchi identities give homogeneous Yang--Mills equations, and variation imposes $\nabla_μF^{μν}_A = J^ν_A$. Chiral fermions arise from a holomorphic Dirac Lagrangian and couple minimally to all gauge fields, reproducing the Standard Model spectrum. Anomaly cancellation follows from holomorphic gauge invariance. A holomorphic adjoint Higgs breaks $G_{\text{GUT}} \rightarrow SU(3) \times SU(2) \times U(1)$ with unified coupling, and a second Higgs breaks electroweak symmetry, generating $W^\pm$, $Z$, and fermion masses. Below the unification scale, couplings run by standard renormalization-group flow. This construction unifies Einstein gravity, Yang--Mills theory, electromagnetism, and chiral fermions into a single classical geometric framework, and admits quantization via a holomorphic path integral that reproduces standard Feynman rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Holomorphic Unified Field Theory of Gravity and the Standard Model Moffat, John. W. Thompson, Ethan. J. General Physics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory We present a holomorphic framework in which gravity, gauge interactions, and their couplings to charges and currents emerge from a single geometric action on a four-complex-dimensional manifold. The Hermitian metric yields on the real slice $y^μ= 0$, a real symmetric metric $g_{(μν)}$ giving the vacuum Einstein equations, and an antisymmetric part $g_{[μν]}$ that reproduces Maxwell's equations with sources. A single holomorphic gauge connection for $G_{\text{GUT}}$, such as $SU(5)$ or $SO(10)$, encodes all gauge sectors; its Bianchi identities give homogeneous Yang--Mills equations, and variation imposes $\nabla_μF^{μν}_A = J^ν_A$. Chiral fermions arise from a holomorphic Dirac Lagrangian and couple minimally to all gauge fields, reproducing the Standard Model spectrum. Anomaly cancellation follows from holomorphic gauge invariance. A holomorphic adjoint Higgs breaks $G_{\text{GUT}} \rightarrow SU(3) \times SU(2) \times U(1)$ with unified coupling, and a second Higgs breaks electroweak symmetry, generating $W^\pm$, $Z$, and fermion masses. Below the unification scale, couplings run by standard renormalization-group flow. This construction unifies Einstein gravity, Yang--Mills theory, electromagnetism, and chiral fermions into a single classical geometric framework, and admits quantization via a holomorphic path integral that reproduces standard Feynman rules. |
| title | Holomorphic Unified Field Theory of Gravity and the Standard Model |
| topic | General Physics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.19161 |