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We have obtained the equilibrium volumes, bulk moduli, equations of state ofthe ferromagnetic cubic $\alpha$ and paramagnetic hexagonal $\epsilon$ phasesof iron in close agreement with experiment using an ab initio dynamicalmean-field theory approach. The local dynamical correlations are shown to becrucial for a successful description of the ground-state properties ofparamagnetic $\epsilon$-Fe. Moreover, they enhance the effective mass of thequasiparticles and reduce their lifetimes across the $\alpha \to \epsilon$transition leading to a step-wise increase of the resistivity, as observed inexperiment. The calculated magnitude of the jump is significantlyunderestimated, which points to non-local correlations. The implications of ourresults for the superconductivity and non-Fermi-liquid behavior of$\epsilon$-Fe are discussed.

Impact of electronic correlations on the equation of state and transport in $\epsilon$-Fe