SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908901143740416 |
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| author | Chkareuli, J. L. |
| author_facet | Chkareuli, J. L. |
| contents | We develop a four-dimensional gauge-gravity unification based on the $% SL(2N,C)$ gauge theory taken in a universal Yang--Mills type setting. The accompanying tetrads are promoted to dynamical fields whose length, when projected onto the background Minkowskian spacetime, is restricted by a nonlinear sigma-model type constraint. This triggers tetrad condensation and spontaneous symmetry breaking, $SL(2N,C)\rightarrow SL(2,C)\times SU(N)$, lifting all noncompact directions. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector, while an Einstein--Cartan linear curvature term is induced radiatively from fermion loops. Below the breaking scale, only a neutral tetrad associated with graviton and $SU(N)$ vector fields remain massless, whereas axial-vector and tensor fields of the entire gauge multiplet acquire heavy masses. The matter sector clearly points to a deeper elementarity of $SL(2N,C)$ spinors, which can be identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out $N=8$. The chain $SL(16,C)\rightarrow SL(2,C)\times SU(8)$ then naturally yields three composite quark--lepton families, while filtering out extraneous heavy states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity Chkareuli, J. L. High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We develop a four-dimensional gauge-gravity unification based on the $% SL(2N,C)$ gauge theory taken in a universal Yang--Mills type setting. The accompanying tetrads are promoted to dynamical fields whose length, when projected onto the background Minkowskian spacetime, is restricted by a nonlinear sigma-model type constraint. This triggers tetrad condensation and spontaneous symmetry breaking, $SL(2N,C)\rightarrow SL(2,C)\times SU(N)$, lifting all noncompact directions. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector, while an Einstein--Cartan linear curvature term is induced radiatively from fermion loops. Below the breaking scale, only a neutral tetrad associated with graviton and $SU(N)$ vector fields remain massless, whereas axial-vector and tensor fields of the entire gauge multiplet acquire heavy masses. The matter sector clearly points to a deeper elementarity of $SL(2N,C)$ spinors, which can be identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out $N=8$. The chain $SL(16,C)\rightarrow SL(2,C)\times SU(8)$ then naturally yields three composite quark--lepton families, while filtering out extraneous heavy states. |
| title | SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2511.19210 |