We investigate the relationship between a one-parameter family of (anti–)de Sitter Yang-Mills models and a model of Einstein-Palatini gravity with matter, realized through Inönü-Wigner contraction of the (A)dS algebra. By setting the group parameter $\alpha$ to zero, the gauge transformation of the potential becomes consistent with the transformation properties of the tetrad form and spin connection. We show that a sector of the Yang-Mills dynamics exists in which the equations decouple. Moreover, a subset of the gauge transformations can be related to diffeomorphisms, leading to the identification of the tetrad field. Finally, the resulting dynamics is consistent with a gravitational dynamics in the first-order formalism.

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• Gauge theories
• Gravitation