Torsion Homology Growth of Polynomially Growing Free-by-Cyclic Groups

We show that the homology torsion growth of a free-by-cyclic group with polynomially growing monodromy vanishes in every dimension independently of the choice of Farber chain. It follows that the integral torsion ρℤ equals the ℓ2-torsion ρ(2) verifying a conjecture of Lück for these groups.