  Motivated by recent experimental realizations of polar metals with broken
inversion symmetry, we explore the emergence of strong correlations driven by
criticality when the polar transition temperature is tuned to zero. Overcoming
previously discussed challenges, we demonstrate a robust mechanism for coupling
between the critical mode and electrons in multiband metals. We identify and
characterize several novel interacting phases, including non-Fermi liquids,
when band crossings are close to the Fermi level and present their experimental
signatures for three generic types of band crossings.
