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arXiv · 2601.19734

A Geometric Action Principle for Unification of Yang-Mills Fields, Gravity and Matter Fermions

Pedro D. Alvarez·Fernando Izaurieta·Cristian Quinzacara
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Abstract

A single geometric action, constructed as a linear combination of a restricted six-dimensional family of Clifford-generated invariant terms, simultaneously generates the gravitational, Yang--Mills, and fermionic sectors and correlates their structure and relative coefficients. The resulting parameter space contains known linearized ghost-free quadratic gravitational models with propagating torsion in a reduced bosonic sector. Our results therefore establish an economical geometric route to gauge--gravity unification that requires neither extra dimensions nor an externally introduced symmetry-breaking field. In particular, the Clifford-algebraic construction naturally accommodates parameter subspaces in which the reduced bosonic sector reproduces known ghost-free theories and the independent Klein--Gordon-type fermionic kinetic term vanishes.

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Pedro D. Alvarez, Fernando Izaurieta, Cristian Quinzacara. 2026-01-27. A Geometric Action Principle for Unification of Yang-Mills Fields, Gravity and Matter Fermions. https://arxiv.org/abs/2601.19734

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