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