Recent progress on QCD inputs for axion phenomenology

The properties of the QCD axion are strictly related to the dependence of strong interactions on the topological parameter theta. We present a determination of the topological properties of QCD for temperatures up to around 600 MeV, obtained by lattice QCD simulations with 2+1 flavors and physical quark masses. Numerical results for the topological susceptibility, when compared to instanton gas computations, differ both in size and in the temperature dependence. We discuss the implications of such findings for axion phenomenology, also in comparison to similar studies in the literature, and the prospects for future investigations.