  The QCD topological observables are essential inputs to obtain theoretical
predictions about axion phenomenology, which are of utmost importance for
current and future experimental searches for this particle. Among them, we
focus on the topological susceptibility, related to the axion mass. We present
lattice results for the topological susceptibility in QCD at high temperatures
obtained by discretizing this observable via spectral projectors on eigenmodes
of the staggered Dirac operator, and we compare them with those obtained with
the standard gluonic definition. The adoption of the spectral discretization is
motivated by the large lattice artifacts affecting the standard gluonic
susceptibility, related to the choice of non-chiral fermions in the lattice
action.
